PHD: Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Techn.

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies PhD by Norbert Palz

Submitted in partial fulfilment of the requirements for the award of the degree of

Doctor of Philosophy

Institute for Design and Communication, Center for Information Technology and Architecture (CITA) Royal Danish Academy of Fine Arts, Schools of Architecture, Design and Conservation, School of Architecture in Copenhagen, Denmark 2012

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

For Sisse

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Colophon Author’s name: Norbert Palz Publication title: Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies Copyright: ©2012 Norbert Palz and the Royal Danish Academy of Fine Arts Schools of Architecture, Design and Conservation School of Architecture ISBN: ISBN: 978-87-7830-289-2 Published by: The Royal Danish Academy of Fine Arts Schools of Architecture, Design and Conservation School of Architecture Philip de Langes Allé 10, 1435 Copenhagen K, Denmark Print: Viaprinto, 2012 Graphic design: Front cover rendering by the author

Supervised by

Prof. Mette Ramsgard-Thomsen, PhD Institute for Design and Communication, Center for Information Technology and Architecture (CITA) Royal Danish Academy of Fine Arts, Schools of Architecture, Design and Conservation, School of Architecture in Copenhagen, Denmark

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Declaration I certify that except where due acknowledgement has been made, the work is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work that has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and ethics procedures and guidelines have been followed.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Abstract The research investigates innovative architectural applications of additive fabrication technologies for the creation of a new digitally defined materiality on the meso- and macro-scales. The thesis investigates tunable mechanical properties created through structural calibration or multi-material composition and represents digital workflows for such methods. The thesis outlines key areas of architectural applications and examines conceptual and modelling representations of an extended performative materiality and how they relate to architectural formgiving.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Acknowledgements The PhD was funded over a three-year period by a research grant from the Royal Danish Academy of Fine Arts in Copenhagen in Denmark and was conducted at the Center of Information Technology and Architecture (CITA) at the School of Architecture. I am very grateful for the generous working conditions the respective institutions provided me during the entire period and beyond.

My heartfelt thanks go to my advisors Professor Mette Ramsgard-Thomsen, Associate Professor Henrik Oxvig and Professor Mark Burry of SIAL, Melbourne, who guided me through a process that was far from linear. Scholarly research in an artistic environment is a process that often comes with unique characteristics different from those of research investigations conducted in natural sciences. Architecture classically orchestrates and conceptualizes knowledge from many disciplines and operates on many scales simultaneously. This entanglement expands the scope of research material and requires continuous adaptation of the research questions and contents to be undertaken, leaving its traces in the psyche of the author. I am very thankful for all of the advisors who steered me through this process.

The research implements findings from material science and structural mechanics and other fields, many of which required costly processes to be undertaken. In this context I am very grateful for the sponsorship I received from the BAM (Bundesanstalt für Materialforschung) in Berlin, FIT (Carl Fruth Innovative Technologien), Objet Inc. and the Universität der Künste Berlin.

I conducted fruitful conversations with Christophe Barlieb, Asbjorn Sondergaard and Bernhard Sommer. Professor Dr.-Ing. Christoph Gengnagel of the Universität der Künste in Berlin proved to be a loyal and supportive colleague on an everyday basis. I would like to express my special gratitude to him.

The practice of a PhD research process affects one’s immediate family and friends. Writing a thesis in two locations—Berlin and Copenhagen—also means a commute that is far from pleasant and quite exhausting. Kaj and Karen Vestergaard-Poulsen generously accommodated me as a long-term guest in their Copenhagen home and were wonderful hosts.

I also owe a great deal to my children Karl, Konrad and Selma for their patience and love.

My deepest gratitude goes to my wife Kirsten, who was loyal and supportive and never let me down. I can never thank her enough.

Norbert Palz Berlin, in December 2011

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Notes to the Reader The text contains several typographical specifications that require explanation. They are used to improve the readability of the text and provide a clearer understanding of its content.

Indented text passages in italics Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

Texts written in this style provide further explanation of a subject and are supposed to illustrate the content. They often contain examples or analogies that I hope will be beneficial for a better understanding of the topic and prevent misunderstandings. During the process of reading these can be skipped and returned later without disrupting the narrative.

Non-indented bold texts Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

Texts written in this style mark important points in the thesis. They are prominently employed in the research question and hypotheses sections especially.

Citations in italics “Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.”

Citations written in this style mark important references to differentiate them from quotations that serve more explanatory purposes.

Citations without italics “Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.”

Citations written in this style are explanatory references.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Table of Contents Colophon ................................................................................................................................................................................................ 4 Declaration............................................................................................................................................................................................. 5 Abstract ................................................................................................................................................................................................. 6 Acknowledgements.................................................................................................................................................................................. 7 Notes to the reader:................................................................................................................................................................................. 8 Table of Contents ................................................................................................................................................................................. 10 Motivation............................................................................................................................................................................................ 13 Thematic Overview ............................................................................................................................................................................... 15 Contribution to Knowledge .................................................................................................................................................................... 18

Introduction…………………………………………………………………….………...….22 1.0

Structure of the PhD ...................................................................................................................................................... 23

1.1 Terminology and State of the Art ............................................................................................................................... 28 1.1.1 The additive fabrication process............................................................................................................................... 28 1.1.2 Application of additive fabrication I: Rapid Prototyping (RP) ........................................................................... 30 1.1.3 Application of Additive Fabrication II- Rapid Manufacturing (RM) ................................................................ 33 1.1.4 Application of additive fabrication III: Rapid Tooling (RT) ............................................................................... 41 1.1.5 Summary ....................................................................................................................................................................... 43

Research Questions I-III and Hypotheses I-III……………….…………………………..44 2.0 Introduction .......................................................................................................................................................................... 45 2.1 Research Question I ............................................................................................................................................................ 46 2.1.1 Digital control and variation of discrete elements through topological rulesets ............................................. 46 2.1.2 Correlating digital design and fabrication for a tunable material design ........................................................... 46 2.1.3 Parameterising natural structures ............................................................................................................................. 46 2.1.4 Material and mechanical complexity ........................................................................................................................ 47 2.1.5 Relevance ...................................................................................................................................................................... 47 2.2 Hypothesis I.......................................................................................................................................................................... 48 2.3 Research Question II .......................................................................................................................................................... 49 2.3.1 Multi-material additive fabrication ........................................................................................................................... 49 2.3.2 Implementation of existing research on functionally graded material............................................................... 49 2.3.3 Finite modelling processes as a design tool ............................................................................................................ 49 2.3.4 Relevance ...................................................................................................................................................................... 51 2.4 Hypothesis II ........................................................................................................................................................................ 52 2.5 Research Question III......................................................................................................................................................... 53 2.5.1 Mirroring historical and contemporary architectural design processes ............................................................. 53 2.5.2 Textile logic and material performance ................................................................................................................... 54 2.5.3 Multi-level design processes ...................................................................................................................................... 54 2.5.4 Relevance ...................................................................................................................................................................... 55 2.6 Hypothesis III ...................................................................................................................................................................... 56

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Methodology…………………………………………………………………………………57 3.0 Introduction .......................................................................................................................................................................... 58 3.1.1 Domain and subdomain ............................................................................................................................................ 59 3.1.2 Global and local transformation............................................................................................................................... 60 3.2 Application in the thesis ..................................................................................................................................................... 64 3.3 Further research methods .................................................................................................................................................. 65

Literature Review…………………………………………………………………….………66 4.0 Organisation of the Literature Review............................................................................................................................. 67 4.1 Literature Review Research Topic I ................................................................................................................................. 68 4.1.1 Identifying the structural component ...................................................................................................................... 68 4.1.2 Auxetic materials ......................................................................................................................................................... 70 4.1.3 Two-dimensional auxetic structures ........................................................................................................................ 73 4.1.4 Three-dimensional auxetic foam structures ........................................................................................................... 80 4.1.5 Critical summary.......................................................................................................................................................... 84 4.2 Literature Review Research Topic II................................................................................................................................ 86 4.2.1 Structural hierarchy and heterogenisation .............................................................................................................. 87 4.2.2 Integrated additive manufacturing ........................................................................................................................... 89 4.2.3 Functionally Graded Materials (FGM).................................................................................................................... 91 4.2.4 Additive fabrication with two source materials ..................................................................................................... 96 4.2.5 Additive fabrication with multiple materials ........................................................................................................102 4.2.6 Performance-oriented material distribution .........................................................................................................105 4.2.7 Critical summary........................................................................................................................................................110 4.3 Literature Review Research Topic III ............................................................................................................................112 4.3.1 From the drawn to the built ....................................................................................................................................112 4.3.2 Digital design and material performance ..............................................................................................................124 4.3.3 Critical summary........................................................................................................................................................128

Experiment I: Graded Auxetic Structures…………………………………………………131 5.1.0 Introduction ...............................................................................................................................................................132 5.1.1 One-dimensionally graded auxetics .......................................................................................................................136 5.1.2 Two dimensionally graded auxetics .......................................................................................................................147 5.1.3 Three-dimensionally graded auxetics.....................................................................................................................159 5.1.4 Conclusion..................................................................................................................................................................175

Experiment II: Heterogeneous Material…………………………………………………..176 5.2.0 Introduction ...............................................................................................................................................................177 5.2.1 Experimental goal .....................................................................................................................................................178 5.2.2 Boundary conditions of the experiment ...............................................................................................................178 5.2.3 Tectonic parameters .................................................................................................................................................179 5.2.4 Definition the material specification method ......................................................................................................181 5.2.5 Defining the manufacturing parameters ...............................................................................................................187 5.2.6 Analysis of the specimen .........................................................................................................................................189 5.2.7 Conclusion..................................................................................................................................................................193 11

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Experiment III: Multi-level Design of Textile Structures with Controllable Material Performance…………………………………………………………………………………195 5.3.0 Introduction ...............................................................................................................................................................196 5.3.1 Geometry, fabrication and material constraints ..................................................................................................197 5.3.2 Weaving ......................................................................................................................................................................202 5.3.3 Experiment Preface: Digitally Knitted Structure.................................................................................................214 5.3.4 Experiment: Computational design and additive fabrication of knitted structures ......................................215 5.3.5 Conclusion..................................................................................................................................................................246

Conclusion and Outlook…………………………………………………………………..248 6.1 Summary ..............................................................................................................................................................................249 6.2 Recommendations .............................................................................................................................................................252 6.3 Final Reflections.................................................................................................................................................................254

Literature ...........................................................................................................................................................................................256 Illustrations and Tables ......................................................................................................................................................................268 Appendix ...........................................................................................................................................................................................272

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Motivation The PhD project started in May 2007 and set out to investigate the impact CAD/CAM technologies, specifically rapid prototyping, had on architectural design practice. A distinct focus was placed on drawn representations, spatial concepts and formal possibilities connected with such processes. This PhD abstract conveyed a thematic openness that allowed the applicant’s personal views on the described issues to come into play.

In my prior architectural practice I had come into contact with rapid prototyping technologies mainly as a tool for the creation of complex models that served to evaluate or present designs, or as a visual/physical analysis tool.

Although the technology has become increasingly prominent within architectural practices for representational purposes in recent years, it had not made any noticeable impact on the building process as such. It appeared that real innovation potentials lay mostly in the advancement of software development rather than in this computer-driven materialization process that showed limited material properties, a constrained production scale and high costs. In addition, the rapid prototyping process was quite resistant to the fabrication constraints of real-world architectural building problems and could allow very easy materialization of models that would be very complicated to erect under real-world conditions. Coming from a professional background that had centred on the realization of challenging three dimensional structures, I was aware that the technology might be misleading in its ability to simplify these possibilities for realization.

The advantages of this technology’s exclusive geometric and fabrication possibilities are intrinsic to its inscribed manufacturing tectonics. They offer unique potential for expanding conventional fabrication options by endowing products with specific properties. These altered boundary conditions, which allowed the materialization of intricate geometric morphologies and took full advantage of parametric modelling tools, could be potentially merged in a basic study on novel building components. This focus on the innovative fabrication tectonics inscribed in the technological process could enrich the world of classical manufacturing methods and pave the way for an investigation of novel architectural applications, material properties and design potentials. This thinking was reinforced by a technological innovation presented by Objet Geometries Inc. in the winter of 2007 that served as an inspirational outlook to future additive multi-material manufacturing and as the key to articulating one of the research questions. The company presented the first printing technology that allowed up to six different photopolymers with varying material properties to be combined for the creation of functional and representative models. This discovery pointed to a field of research that could investigate the calibration of computationally defined materials, in terms of either the structural properties or material composition, and hereby take advantage of a broad spectrum of digital tools in a novel way. This prospect would assign to the manufacturing technology a radical new function unprecedented in architectural and fabrication history. This research would also allow a natural implementation of the institute’s research interests in drawing and representation protocols related to the technological innovation, since the calibration of these synthetic material properties would require innovative representation and conceptualization of these changing properties.

An inspection of the historical technological developments of additive fabrication conducted in the early phase of my PhD research revealed an impressive development cycle proceeding from raw proof-of-concept experiments towards a reliable technology for small to medium-scale artefacts within 30 years. A parallel look at the rapid development of architectural software in the last 15 years pointed to similar development cycles that supported a future vision of an expanded architectural practice engaged in potentially emerging shifts of their basic boundary conditions. An 13

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

historical, time-sequenced assembly concept that connects architectural functionalities with discrete geometric and material units could thus be transformed by an interwoven planning and building process that could potentially integrate multiple functionalities in a single component. The historical concept of a “building skinâ€? could potentially be related more closely to the richness of expression and to functional materials with structural hierarchies found in nature, and foster a new kind of interaction between architecture and its users. On a constructive level, merging multiple building functions into a single additively fabricated component appears achievable on the basis of these investigations. The assembly timeline, which is usually coordinated by erecting a primary load-bearing structure and is followed by a sequence of subsequent building elements that then shapes the appearance of the buildings around us, can potentially blend multiple functions in a new construction component whose dimensions are based on building chamber-sized components of the manufacturing technology. Formal complexity and ease of assembly through new joinery systems can be achieved in this way. Technological complexity migrates from structural assemblies to material specifications that assume the role of performance control. Structural morphologies could then be guided by procedures to optimize shape and topology and thus integrate material economy into the practice of building the load-bearing core of the project. This rethinking of architectural, structural and material practice holds great promise ‌and manifold technological challenges.

These future interfaces can develop a new formal language that is defined by these enhanced functionalities and the geometric possibilities presented when the technology begins operating on the building scale. Once these manufacturing methods have achieved reliable production quality standards and more competitive prices, heterogeneous load-bearing systems could compete with conventional structural solutions while communicating an innovative tectonic language, design method and theoretical implication. Such created structures could expand the historic repertoire of classic load-bearing systems like beam and column with a locally specific tectonic expression using a minimum of material and integrating structural performance.

A reflection upon these innovative aspects of a calibrated materiality that is generically interwoven with digital design and additive fabrication holds the potential to continue a material-related historical discourse within architecture from a contemporary, computer-driven perspective.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Thematic Overview The thesis is conducted as an experimental investigation on the computational design of material properties and the additive fabrication of such in the context of future architectural formgiving. These material experiments are accompanied by research on the digital representation and mechanical characteristics of this innovative materiality and the deduced performative and morphological conception of architectural elements it can yield.

The field of additive fabrication that lies at the core of this research has proliferated in recent years due to improvement in the mechanical properties, greater material diversity, more economical on- and offline printing solutions, and the scale of the artefacts that can be produced. Additive processes that create fully functional objects utilize the known processoral advantages that have been inscribed in the technology since its appearance in the late 1980s: •

The generation of manufacturing data is inherently based on a process of slicing 3D information; the

achievable production tolerances remain invariant towards the complexity of the sliced object. •

The manufacturing tectonics allows the production of geometrically complex objects that are impossible to

realize in conventional manufacturing processes. •

The creation of data is based on CAD tools. The outcome of additive fabrication is therefore tightly

connected to the abilities of the software packages employed.

Yet today only few additive fabrication technologies exist that show potential financial and spatial applicability for architectural purposes. The additive fabrication of functioning components of highly complex structural and material composition will require a phase of wider interdisciplinary experimental investigations in the coming years. The first signs indicating such potential developments have come from research on additively fabricated building-scale parts conducted by several private and academic institutions. Technological progress is complemented by recent standardization efforts for process and material quality through academic institutions and industry, which could help to promote more widespread utilization of additive fabrication components in the building sector in the future.

Newly developed file formats that incorporate gradual material distribution, better mesh descriptions and smaller file sizes demonstrate a growing interest in the industrial sector to expand the application of additive fabrication technology as a manufacturing technology with real-world applications.

Interdisciplinary connections between different technologies have already proven crucial for the initial invention of additive fabrication technology. These different technologies (like laser engineering, numeric control of machine paths and their hardware counterparts) unfolded into a new manufacturing tectonics of materialised striated information, which has characterized additive fabrication since its beginnings and represents the only continuous element within the now shifting technological boundaries. Such confluence of different technological streams will eventually merge additive fabrication with other technologies into a new future manufacturing system with innovative properties and scales. The thesis points to potential fields for such technological interconnections that can grant a promising perspective for complex multifunctional material composites and in which additive fabrication can play an important role.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

For this reason the experiments are designed methodologically and conducted in a two-fold fashion: on the one hand as investigations within the concrete computational and fabrication boundaries, and on the other as experiments that allow their findings to be transferred to the future conditions of technology transformation in that field. The computational descriptions are hence defined as topological relations that allow implementation on different fabrication scales under the required structural constraints. From a fabrication point of view this aspect is enforced by concentrating on the generic properties that represent the crucial and most persistent advantages of additive materialization, independent of the specifics of individual additive manufacturing procedures.

The PhD research presented here contributes to an interesting segment of contemporary additive fabrication investigations, which explores the calibration of the material itself with regard to its structural performance and composition control, and which builds upon research from material science and structural mechanics under the novel fabrication tectonics. The computational solutions in the process of development by the author and others provide for the control and calibration of irregular digital geometries across multiple manufacturing scales and—as such—advance the core properties of additive fabrication in tailored morphological resonance on a local spatial level.

Theoretical questions within architecture arise from these potentials, which challenge the conventional understanding of the character and functionality of materials and require these new potentials to be implemented and represented in workflows with distinct traditions and characteristics. The digitally driven calibration and construction of novel structures and formations envisioned here alters the historical dialogue on the coherency between material, structural and form that has been conducted since Aristotle, Scamozzi, Violet-le-Duc and L. Kahn, among many others. The conceptual approach between construction typology and material use that persists in architectural history is about to shift once more. Architectural designs in the future may no longer be based on the best fitting structural solution for a given material with more or less known properties, but by a reverse process that tailors an appropriate material with graded, unique characteristics to a chosen form and performance.

The digital control over a material’s mechanical behaviour at stake in this thesis is defined by structural properties that act on various scales. On the molecular scale, spatially assembled linear, branched and cross-linked polymer chains determine diverse mechanical and physical properties of a material such as stiffness and viscosity. Structure can appear in meso-scale formats as fibres and cellular clusters that lend isotropic and anisotropic mechanical properties, among others. Macro-scale formations represent the highest point of the structural hierarchy and drive the performance of objects created in this way with respect to the properties of their lower meso- and micro-scale conditions. The first two experiments thus approach the control over mechanical properties by differentiating the scale on which the computational design of structural differentiation takes place.

The first experiment takes a single manufactured polymeric material that is spatially assembled in a geometric envelope whose macro-scale structural layout is then responsible for the desired performance. The macro-scale formations consist of digitally parameterized auxetic cells in 1D, 2D and 3D, which control the expansion and contraction under stress and strain in a counterintuitive manner. The behaviour of the printed samples thus created is traced not on the basis of a mechanically complex assembly, but defined solely through the digitally controlled complexity of its geometrical layout in interaction with the material applied in the printing process.

The second experiment concerns a periodic macro-scalar geometric envelope that achieves mechanical performance through a composite interaction of molecularly differentiated manufactured materials with varying elasticity. The experiment takes advantage of recently developed multi-material printing solutions that provide access to up to 14 16

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

mechanically differentiated print materials. The composition control of these materials within the periodic geometries utilizes structural analysis tools like a design driver that coordinates the sorting process.1 The integration of digital design, fabrication and tunable material performance derives from a novel design protocol that allows new and autonomous architectural conceptions of form, structure and morphologies to emerge. Complex geometrical, numerical and structural influences act upon topologically defined digital geometry definitions that materialize through additive fabrication. The third and final experiment investigates these derived novel morphological, material and processoral aspects of architectural formgiving in relation to additive fabrication with the help of the structural logic of textiles, in particular knitting. The systematic and geometrically controllable nature of the individual threads allows a feasible field for computational translations, while constituting an application for additive fabrication techniques that is interesting due to their high degree of detail, and highlights the key advantages of this technology by allowing local variations and modification in many materials. Textiles can visualize the conceptual implications of this design process that interweaves computational geometry and dynamic material performance through a new definition of what architectural form can be. The geometrical process applied in this experiment represents a departure from the Euclidian geometric protocol, blending different hierarchical levels of formgiving information into an interconnected tissue of computational, mathematical and artistic origin with different design interfaces. The new interconnection between material, structure, form and the design process discussed here is naturally confined by a digital toolset, but at the same time picks up on a topic that has persisted within architectural investigations over many centuries. So the introduction of projective geometry in the 15th and 16th centuries had changed architectural design by directly combining the design process with representation and fabrication information. The last experiment re-addresses this historical phenomenon in the light of contemporary digital processes and draws conclusions about its conceptual impact, which resulted in a distinct—but short-lived— typology of new architectural elements.

At the beginning of the research period most of the above mentioned topics had received only sparse attention among architects and a few material scientists, but growing attention is visible today. Despite the mentioned technological limitations, both present and continuing, this new research terrain presents manifold questions that await investigation in the coming years in an interdisciplinary approach adapted to the improving technological boundaries of fabrication, computational design and digital simulation. The scope of different knowledge fields required to develop sensible solutions provides a natural substrate for fruitful interdisciplinary work that entwines the understanding and interests of architects, material scientists, theorists and others in a joint approach.

1

In the thesis text the first two experiments are nevertheless thematically differentiated into material research on tunable

structural and material composition. This simplification does not account for the persistency of the structural impact over multiple scales, but is done for the sake of easier differentiation.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Contribution to Knowledge Architectural development in history was often related to innovations in building technology and the discovery of new materials. So cast iron revolutionized the architectural repertoire through its lightweight and efficient framework; later, reinforced concrete allowed large spanned structures to be erected with simultaneous stress and strain load-bearing capabilities, and new building typologies to unfold. This PhD is engaged with a research question that examines further consequences of the impact of digitalisation within architecture, which can be expanded to the material itself and the design procedures and conceptions of structures that it makes possible. Although limited in their scale and mechanical properties, additive fabrication procedures show enough potential to encourage such research on the derived architectural consequences and their envisioned impact. This engagement with material properties and their associated design procedures will lay the groundwork for later more potent technologies and scales on which they can be applied.

A retroactive look at historical precedents supports this approach. The first civil engineering structures that were created after the invention of cast iron in the 18th century still applied structural principles of masonry and timber constructions rather than taking full advantage of the structural properties the new material made possible for the formal repertoire of architecture.

Consequently, the structural comprehension that the load-bearing functions of steel would differ from those of wood were not reflected in new distribution systems, in the tectonics of its structural members, or in novel assemblies of such. In the classic example of the Coalbrookdale Bridge2 one can witness this misguided application in the fact that the joints of the iron members are designed as wooden connections, and thus contained structurally redundant components (Billington 1985, 39).3 Even subsequent building projects relied heavily on the historical knowledge that had been inherited from wooden crafts.4 In order to understand the consequences of this process, a phase of broader experimental investigation should be conducted in the coming years to assess the promise of a new construction typology fuelled by the new material specifications emerging from a lively technological environment and computational developments. The benefit of the activity conducted here lies in an anticipatory understanding of the emerging conceptual design challenges that are likely to proliferate due to improved mechanical properties and to the greater material diversity and scale of the artefacts produced by means of additive fabrication. The promise of this activity lies in establishing congruence between the technological development and design conceptualization to allow a faster and more consequent implementation of gained knowledge in the architectural design process.

It is obvious that this work is just the beginning of a longer research process that will take decades. Inevitably, technological innovations will occur, creating boundary conditions for additive fabrication different than those valid today. This research therefore focuses on highlighting those characteristic aspects that have surpassed the individual innovations of the last twenty years and thus show greater potential than short-term technological innovation. The methodological chapter specifically addresses methods and parameters that investigate this aspect.

2

Designed by Pritchard, Davidson and Darby III in Coalbrookdale, Shropshire, West Midlands, UK from 1777-79.

3

One of the first examples of a cast iron bridge that took full advantage of the material’s mechanical properties in its structure

was the Bonar Bridge in Scotland, with a 45.5-m arch designed by Thomas Telford. For deeper insight into the early developments in the civil engineering and manufacturing of bridges of this period see Billington 1985.

4

Troyano writes on this issue, “Yet it was not long before web girder bridges, either lattice or trusses were built; the latter two

were the direct result of timber beams which also had been used previously.� (Troyano 2003, 295).

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Contributions I+II: Graded materiality in structure and composition Architectural design often has to negotiate an envisioned form with material-specific mechanical properties that must be aligned with a larger structural system. Additive fabrication, by contrast, allows a new design process to emerge, one that considers material not as a homogenous property whose traditional application is based on centuries’-long practice, but rather as a unique and variant structural constellation of matter in space. Traditional structural engineering is based on a calculation of continuous material properties that are assigned to the load-bearing members of construction. Additive fabrication processes could develop materials in which these structural properties are in flux, migrating from isotropic to anisotropic behaviour in three dimensions. The boundary conditions for the local material specifications could be then extracted from a goal-oriented calculation of the structural requirements of a synthetic material to be defined later, which would realize the desired performance through material grading and structural composition or a combination of both.

Contribution The research will deliver methods to design three-dimensionally heterogeneous material properties: •

Through variant calibration of the internal meso-structure of materials with novel form-changing potentials

•

Through computational composition of multiple materials whose selection is derived from a finite element process.

•

Through a multi-layered digital design method for additively fabricated textiles based on planar and cellular logic

The research will provide insight into the structural calibration of form-changing potentials through applying material research conducted on auxetic, functionally graded materials and on textiles to the digital context of additive fabrication.

Contribution III: A novel design protocol Additive fabrication introduces a different relationship between manufacturing tolerances and achievable geometric complexity. In this process the complexity of the object as regards digitally defined geometrical detail can be increased without a simultaneous increase in manufacturing time. This independence between geometric detail and manufacturing time represents one of the key innovative properties of the technology. The underlying mathematical procedures employed for digital design processes expand the classical—pre-computational—scope of architectural geometry protocols, like descriptive and Euclidian geometry, which served for centuries as the ruling paradigms for an architect’s design practice. These potentials that lie embedded in emerging computational workflows and fabrication properties will be investigated so that their full benefits can be exploited in later architectural design processes and their productions.

Contribution The thesis correlates recent developments in additive fabrication with an altered design practice of high abstraction and material engagement. Incremental complexity of form on a growing scale entails significant changes in the way architectural solutions will be conceived, designed and manufactured in the future. The text argues that this development has parallels in the Renaissance period, which shifted 19

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

architectural design from descriptive to projective geometry and revealed consequences for a formal vocabulary of architecture and perception of objecthood that led to the emergence of a geometrydependent manufacturing protocol liberated from representative aspects of the drawing process. This historical analogy is mirrored to contemporary digital design processes, so that questions about the character of future design protocols can be derived and a novel understanding and relationship between form and structure can be deduced.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Introduction

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

1.0 Structure of the PhD The PhD thesis is composed of six individual chapters: 1.

Introduction

2.

Research question and hypothesis

3.

Methodology

4.

Literature review

5.

Experiments

6.

Conclusion and outlook

The following text will give a brief summary of the chapters and explain how the different parts of the text are connected.

Content of Chapter 1.0: Introduction The first chapter describes the technological boundary conditions of additive manufacturing processes and presents innovative principles that expand the scope of conventional fabrication processes. It introduces the state of the art of additive fabrication and points to key research and applications in architectural, engineering and medical workflows, among others. The introduction will define a nomenclature for Rapid Prototyping, Rapid Manufacturing and Rapid Tooling processes based on specific applications, which will be used throughout the entire thesis. Where necessary, further specifications of individual technologies will be presented later in the text to provide a more detailed account of the procedures mentioned in the first chapter. This more descriptive character represents the author’s selection from the vast field of contemporary research being conducted in the fields of additive fabrication and computational design; by its very nature it must remain fragmentary so as not to go beyond the scope of this work. It should nevertheless point to the adaptivity—shown in in multiple exemplary applications—of the ruling tectonic and geometric principles that are generically embedded in this new fabrication methodology. The selected material should provide an understanding of the foundations of research on which the experiments will build.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Content of Chapter 2.0: Research questions I-III and hypotheses I-III Three research questions are developed through an analysis of the previously defined technological boundary conditions and structural specifications. The technological investigations centred on an innovative application of the manufacturing technology are correlated with a proposed architectural design practice that evolves out of the combination of digital design processes, manufacturing technology and material engagement. The research questions are posed as follows: Research question I: Can additive fabrication be employed for the rapid manufacturing of cellular materials with tunable properties based on digitally calibrated structural variation?

Research question II: Can additive fabrication be employed for the rapid manufacturing of cellular materials with tunable properties based on digitally calibrated material variation?

Research question III: Can additive fabrication processes for tunable material composition and multi-level digital design create a new design protocol and characteristic tectonic typologies?

The character of the research questions calls for application of a two-fold strategy to the experimental investigations.

The research questions address concrete problems of material design and additive fabrication that require a novel application of computational tools to control the material properties known from related manufacturing processes other than additive fabrication. The thesis also correlates these findings to an architectural workflow and its impact on a material engagement and preconception of form that expands a historical dialogue on the correlation between geometry, fabrication and structural performance.

Definition of three hypotheses The formulation of the research questions leads to the definition of three distinct hypotheses to test in the following experiments. Each experiment will correlate the findings with the proposed hypothesis in a paragraph concluding the respective chapter. All three conclusions will be conflated in the closing chapter of the thesis.

Hypothesis related to research question I The first hypothesis claims that material performance can be calibrated digitally by locally altering the structural properties of a single material. Integrating research conducted in neighbouring fields of material research and structural mechanics allows new knowledge to be implemented into digital workflows and manufacturing streams to produce materials with counterintuitive properties that take advantage of the novel manufacturing principles of additive fabrication.

Hypothesis related to research question II The second hypothesis claims that a three-dimensional material heterogeneity can be developed by means of a digitally derived material composition that takes advantage of recent advancements in multi-material additive fabrication processes. The hypothesis states that structural analysis processes can be employed in reverse as design 24

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

drivers for the calibration of three-dimensional selections of different materials with varying elasticity properties to produce materials with gradual, tunable mechanical properties.

Hypothesis related to research question III The last hypothesis claims that through the integration of additive fabrication processes and computational tools a novel form of design practice can evolve with innovative and characteristic tectonic morphologies. This process encompasses a different approach to the formal preconception of architectural elements, expanding the scope of the Euclidian geometry protocols predominant in architectural practice for centuries in favour of a multi-level design process with novel interfaces and drawing protocols.

Content of Chapter 3.0: Research methodology The research presented centres on a technological environment that is defined by expanding possibilities of computational geometry and the proliferation of a novel manufacturing technology. The text will strive to develop a conceptual methodology that locates individual technological innovations within a larger complex of interdisciplinary connectivity that can unfold into sudden manufacturing and design innovations. Technological development can hereby be understood as a continuous development process of global technological conditions through incremental local technological innovations with distinct properties. A portrayal of these specific local properties and the technological origins of additive manufacturing was therefore explained in the introduction. This dynamic arrangement and projection of interdisciplinary research requires a broader integration of many disciplines that could be employed, in direct or modified applications, to define a research strategy. This approach will be reflected in the selection of multidisciplinary references for the literature review and the implementation of experiments, which draws upon findings from fields as diverse as mechanical engineering, material science, structural simulation techniques, textile research, and even architectural history and philosophy, which are projected onto the distinct research objective.

This overarching methodology is coupled with experiment-specific testing methods elaborated in the description sections of the respective experimental chapters.

Content of Chapter 4.0: Literature review The individual thematic research areas will be portrayed and discussed through key publications and research developments in the form of a literature review that complements the previous introductory chapter more specifically, relating the work already performed on each research question and the proposed hypotheses that frame the three experiments. This literature review serves as a specific introduction to the scientific and theoretical boundary conditions that have been applied to the respective topics to date and elaborates the state of the art upon which the later experiments build.

Review of literature related to hypothesis I The literature corresponding to hypothesis I projects interdisciplinary research conducted in the field of material science to contemporary processes of additive fabrication using calibrated mechanical properties. The paragraph will portray and evaluate contemporary and historical research on auxetic materials with 1D, 2D and 3D performance.

The experimental section examines and translates these properties to digital parameterization potentials that can be applied for a digitally driven bespoke materiality.

25

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Review of literature related to hypothesis II The literature corresponding to hypothesis II investigates contemporary and historical research on functionally graded materials in two and three dimensions. The text critically examines applications of innovative multi-material additive fabrication processes that have been employed to calibrate structural and material performance through multimaterial interaction. The text will project findings from manufacturing research, finite element-based analysis and design processes for the calibration of such materials onto additive fabrication and outline their potentials and remaining constraints.

Literature review related to hypothesis III The last part of the literature review will analyse the impact of additive fabrication on contemporary computational and manufacturing processes of architectural formgiving through historical analogies. The historical shift in the design protocol from Euclidian to projective geometry that took place during the Renaissance period introduced a novel geometrical toolset to the world of architecture, which bears similarities to the processes researched here.

Projective geometry provided representation, design and manufacturing instructions in a single drawing format that led to a new building typology and an altered practice of formal variance with proto-parametric properties. The correlation of these two streams of design development should establish a larger perspective on architectural progress that integrates, mirrors and reflects upon contemporary processoral, design and conceptual developments in a historical continuity of knowledge generation. This overarching approach that constitutes the basis of the research is outlined in greater detail in the methodological chapter.

Content of Chapter 5.0: Experiments I, II, III Three experiments are developed that implement interdisciplinary research in correlation with innovative computational design strategies and the manufacturing conditions of additive fabrication to design materials with heterogeneous properties. Each experiment develops physical prototypes that are tested and documented in various media. The methodological approach portrayed in the previous chapter carries out an application in the chosen experimental setting, drawing on the references employed by the individual experiments. For the specific testing and design procedures of the experiments additional methods are applied, the specifics of which will be explained in the relevant sections. The experimental results are discussed in a conclusion at the end of the chapter.

Experiment I The experiment investigates 1D, 2D and 3D auxetic materials with tunable form-changing potential. Auxetic materials show counterintuitive properties that have been investigated in metallurgy and are transferred in this thesis to mono-material additive manufacturing processes. What makes the mechanical performance of auxetic materials special is that they operate under stress and strain in a reverse manner, expanding under stress and contracting under strain, in contrast to materials with a positive Poisson ratio. The local calibration of these properties is achieved through digitally parameterized structural differentiation.

The creation of auxetic structures with a gradual distribution of negative Poisson values can expand the scope of available bespoke material performance, assigning local control via unilateral, bilateral and trilateral compression and expansion through calibrated auxetic behaviour. This graded performance allows a finer control of materialintegrated movement control in an auxetic performance over one, two or three axes and could be potentially employed as a novel system for controlling the movement and curvature of structures.

26

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Experiment II The experiment employs additive fabrication techniques to create different test specimens that are supposed to deliver differentiated performance through specification of their internal material distributions. The experiment geometrically defines a material that has three-dimensionally heterogeneous and gradient distributions of stiffness values. The experiment expresses such three-dimensional heterogeneity through material differentiation while maintaining a periodic structural composition that is locally invariant.

This novel material property can be created using recently developed multi-material additive fabrication options that allow a three-dimensional distribution of mechanically differentiated cells. The experiment uses structural analysis software to create a 3D heterogeneous performance profile that is responsible for the internal material distribution and the deduced gradual distribution of the mechanical properties within the test specimen. The experiments project related design and testing methods from two-dimensional functionally graded materials (FGM) to multi-material additive manufacturing processes that generate FGM materials with heterogeneity in three dimensions.

Experiment III The experiment investigates a new design protocol that is emerging from digital design processes, manufacturing technology and material engagement based on the example of textile structures. The first test investigates planar woven structures and moves on to cellular structures like knitting. The experiment is to demonstrate that additive fabrication and digital design processes can be employed to create a novel understanding of a multi-level design practice and formal domains, which integrates a plethora of input sources with tunable structural behaviour of additively fabricated artefacts.

The experiments test varying allocations of input sources relevant for structure and formgiving to demonstrate that applying them at different process locations allows a topologically encoded structural matrix to be activated and shaped in numerous ways. Thus an innovative morphological result can be produced that allows a novel material performance to emerge from additive fabrication processes. The tests conducted will work with a spatial system of interlocked linear elements whose assembly sequence is derived from textiles. Computational translations of textile geometries will be tested in a digital and physical model and the geometrical constraints of these techniques will be described. The chapter delivers an argument that such multi-layered design processes can show enough conceptual flexibility to allow the realisation of performance-oriented but also less utilitarian approaches.

Content of Chapter 6.0: Conclusion and Outlook The final chapter of the thesis will conclude the research process with a joint critical correlation between the different research hypotheses and the experimental results. The chapter identifies existing constraints that must be overcome and develops an outlook for future research. This outlook also offers guidance for potential applications and the scale of building components as well as related novel design processes that could be beneficially integrated to facilitate implementation into an architectural workflow that takes advantage of a digitally calibrated materiality in a novel fashion.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

1.1 Terminology and State of the Art Computer aided manufacturing (CAM) technologies can be differentiated into subtractive processes, e.g., 3-5 axis Milling, Laser or WaterJet cutting, in which material is removed by a tooling device from a given volume; and additive processes, which produce a part through the controlled, layered assembly of material. Each of these manufacturing principles delivers a specific physical tectonics of the created object, which is derived from the tooling principle applied and operates under distinct geometric constraints that have to be taken into account during the design process.

Subtractive methods that cut or grind away layers of material can be interpreted as an enhancement of a traditional toolset of material handling. Milling technologies can be seen as automated carving processes; computer-guided cutting thus replaces the former process of laboriously separating material with knives or bladed instruments.

Through technology, the historical characteristics achieved by the manual reduction of material now have been extended, amplified and refined through higher mechanical precision, larger scales, faster production cycles and a broader choice of materials, in which the human is engaged as a control and design instance.

Additive fabrication introduces an entirely new fabrication process with its own characteristics. “Additive fabrication” is thus a collective term for a series of manufacturing processes that allow the vertically layered materialisation of three-dimensional digital content in a broad variety of materials ranging from polymers, plaster, biodegradable materials to metallic alloys and others. Additive fabrication procedures can be differentiated into Rapid Prototyping (RP), Rapid Tooling (RT) or Rapid Manufacturing (RM), depending on the intended application of the finished object.

The term “additive fabrication” will be used throughout the thesis to designate this specific layer-based manufacturing principle in accordance with the recently confined ATSM standard (ASTM International 2010).

1.1.1 The additive fabrication process The geometric complexity of the digital volume model to be fabricated in such a process can be quite high and allows very detailed objects to be printed in a similar amount of time as simpler geometries, since the volume is constructed from vertically arrayed cross-sectional layers of materials in a chronological sequence. In an automated process the digitally designed or externally collected5 watertight mesh geometry is sliced into thin layers of as little as 16µ on the z-axis, depending on the technology applied.6 The volumetric geometry has to be watertight and comply with minimum build sizes of the fabrication technology to deliver a successful result. Surfaces should contain triangular or quadrangular mesh-faces with matching edge vertices and uniform distribution of their discrete normals.

5

For instance, geometric information can be retrieved from CT data for medical prototyping, see Wanga, Wang and Lin (2010),

other options include reverse-engineering physical models (M. Burry 1998) 6

This resolution does not represent the finest layer thickness achievable today in commercial fabrication technology, but rather an

average that can be achieved by most rapid tooling manufacturers. The finest resolution achievable today with a commercially available additive fabrication machine is a layer thickness of 0.06mm (EOS u.d.). The EOSIT P760 can produce thermoplastic parts in that resolution up to a size of 580mm x 380mm x 580mm.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Non-uniform rational B-spline (NURBS) geometries have to be translated into polygon meshes to be printable. As the definition of the mesh resolution determines how the initial NURBS geometry is approximated, it must be chosen such that it can provide for a smooth surface curvature flow. Accordingly lower mesh resolutions lead to facetted geometries that alter the initial form.

The classical file format for additive manufacturing is the Stereolithography file (acronym *.stl.) This format, invented twenty years ago, contains the geometric specifications for the mesh (including surface-normals and three/four coordinate points) but is restricted in implementing other potentially viable information (like colour, texture and material variation) that cannot be inscribed yet. The layered information extracted from the *.stl file is translated into a mechanic movement of the manufacturing unit, which contains a servo-driven print head or a laserpowered light source that starts the sequential build process layer by layer in the z-direction.

In March 2011 ATSM introduced the additive manufacturing file format (*.amf) based on previous research by Hiller and Lipson (2009) to replace the historical *.stl protocol, introducing colour and material properties, texture maps and graded material specifications that are created through a blending ratio of different print materials. AMF files also allow the detailed geometric description of curved mesh triangles, which are specified by defining an additional normal vector in the centre point of the triangle. The file generated is usually half the size of a comparable compressed *.stl file. (ATSM 2011).

Certain 3D modelling tools further allow the direct retrieval of the layered information from the digital NURBS or mesh model in form of a *.slc or *.cli file format. These formats have to be correlated to the final printer resolution with regard to the z-values of the layers when they are retrieved and can be extracted from mesh and NURBS geometries alike.

Since a complex surface is cut into individual vertical areas, complex geometries are broken into a freeform area of material that is locally hardened by an appropriate mechanism. Usually the built layer is lowered by the thickness of the next layer, and the process is repeated until the model has been completed. Overhanging geometries are stabilized by a support structure or a powder bed that must be removed mechanically and often can be reused for the next print process. Powder-based processes use a print head with a binder solution that is locally ejected; polymerbased processes employ a laser unit for sequential or simultaneous hardening of the respective sections of the fluid build material and support structure. Other processes like Fused Deposition Modelling (FDM) or the FAB@Home printer unit eject polymeric slurry through a valve that fills the perimeter area of the horizontal section and immediately hardens in open air. These processes have additional support structure material that is released from a secondary valve, which has to be removed after the print procedure has been completed, and constrains the object’s geometric boundary conditions with regard to minimum build dimensions.

Maturing technologies allow now the production of functional near-net shape7 parts with properties that are impossible to realize with conventional subtractive methods, and it is expected that the process will be further strengthened through refined manufacturing resolutions, more durable material properties and powerful computational practices. The application of these technologies has been expanded continuously since its innovation in the late 1980s, while maintaining its unique manufacturing features. A larger-scale implementation of this manufacturing technology is desired and encouraged (see Bourell, Ming and Rosen 2009). Material and processoral

7

“Near net shape� defines a manufacturing tolerance that is close to the digital source geometry and requires little refinishing. In

additive fabrication processes this quality is defined by the fabrication technology employed and the local curvature of the geometry.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

standardization efforts are under way to further expand implementation into industrial and potentially architectural production cycles.8

1.1.2 Application of additive fabrication I: Rapid Prototyping (RP) Rapid Prototyping is a group of technologies that follow the additive fabrication principle of layered material assembly. Common synonyms include: 3D Printing, Freeform Fabrication, Solid Freeform Fabrication, Layered Manufacturing and Stereolithography. Yet most of these are imprecise.

The application of RP is generally restricted to representative or model functionality. Medical prototyping can serve as a training and didactic tool for complicated medical operations (Suzuki et al. 2004), (McGurk et al. 1997) and the functional testing of rapid manufactured prostheses through coupling with CT data. Industrial design uses the technology for product development in scale and for basic functional testing (Avrahami and Hudson 2002).

The first commercially available rapid prototyping machine, called SLA-1, was developed in 1988 by 3D Systems (Rock Hill, SC). The technology was coined “Stereo Lithographic Apparatus” and operated with local UV laser-based solidification of a liquid photopolymer resin to generate parts. The stereolithographic process was abbreviated SLA and was patented in 1990 by Hull (1990). Today SLA, along with “Selective Laser Sintering” (SLS), represents the most prominent RP technology for high-quality, large-scale objects using a broad spectrum of materials. The concept of a layered assembly of material, based on a digital model, nevertheless already existed long before 3D Systems’ first machine was developed. In 1971 Wynn Kelly Swainson filed a patent for a manufacturing system that contained the key elements of the later SLA technology. His patent was finally approved in 1977 and described a “Method, apparatus and product in which a three-dimensional figure is formed in situ in a medium having two active components by causing two radiation beams to intersect in the media. The dissimilar components are selected to respond to the simultaneous presence of the beam and to either react or to produce reactants which render the intersection of the beams physically sensible or distinguishable. The beams trace surface elements of the figure to be produced.” (Swainson 1977) 1991 saw the arrival of three new additive technologies: Fused Deposition Modelling (FDM), Solid Ground Curing (SGC),9 and Laminated Object Manufacturing (LOM).10 A year later Selective Laser Sintering (SLS) became available on the market. The technology was originally developed at the University of Texas, and patented11 in 1989 by Carl Deckard and commercialized by DTM Corporation, now 3D Systems. The SLS rapid prototyping process uses the heat of a CO2 laser to “sinter” or melt powdered thermoplastic materials at high temperatures, but powdered materials such as ceramics and metals are also feasible in layers of 0.1mm-0.15mm. The CO2 laser is guided across the part bed by a scanning system and “selectively” sinters or melts the material based on cross-sectional slice information from the 3D CAD data file. The parts are built in an atmosphere that controls the thermal distribution and thus requires very little laser power to sinter the material.

The powder in the build chamber acts as a support for the part during fabrication and no additional support structure is 8

An unpublished proposal for ISO classification of additive fabrication processes headed by the manufacturer EOS GmbH and

DIN (Deutsche Industrie Norm) can be found here (EOS GmbH/Deutsche Industrie Norm 2010).

9

The SGC process uses photosensitive resin hardened in layers similar to stereolithography. The SGC process is considered a

high-throughput production process as each layer of photosensitive resin is hardened immediately.

10

In the LOM process cross sections from a digital model are cut from paper using a laser. The paper is unwound from a feed

roll onto the stack and first bonded to the previous layer using a heated roller that melts a plastic coating onto the bottom side of the paper. Waste paper is wound on a take-up roll. After a period of technological stagnation, LOM-based manufacturing technology has been further developed recently by Mcor Technologies (2011).

11

Deckard 1989 30

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

required. SLS is able to produce large parts with tolerances and detail similar to SLA, but with the added advantage of strength.

The development of the rapid prototyping technology continued with the release of 3D printing technology developed by Stratasys and Z-corp. in 1996. Stratasys distributed a wax-like material, while Z-corp. employed starch- and plaster-based powder materials and a water-based liquid binder. Both materials were ejected through a print head in a layered movement.

Further development in servo engineering, material science and the numerical control of machines broadened the spectrum of available manufacturing processes and materials to include resins, plaster, paper, wax and plastics,12 but also ceramics and quartz sand. The respective choice of the material and technology influences the stability, size, post-treatment and price of the model. Rapid prototyping technologies are therefore usually differentiated by their build process and material.

The most common contemporary RP techniques are Selective Laser Sintering (SLS), Stereo-Lithography (SLA), Digital Light Processing (DLP), Fused Deposition Modelling (FDM),13 Jetted Photopolymer (JP), Multi Jet Modelling (MJM), and 3D Print.14 In 2008 Objet Geometries Ltd. (Sagi 2007) introduced the first multi-material polyjet print process, which allowed the fabrication of 3D objects built up by as many as 14 materials. The company provided a range of resins that were differentiated in their visual or mechanical properties and utilized a multi-jet process with light-hardened polymers (Objet Geometries Ltd. 2010). In the process a predefined blend between the two source materials was determined that would allow multiple materials to be used in a single model. Each of these materials has specifically addressable material properties that can be geometrically assigned to a volumetric piece of 3D geometry within the model. The research addresses the exact boundary properties of this specific technology and other attempts to generate artefacts with multiple materials in Chapter 5.2.5, Production parameters.

Conventional RP models usually have a monolithic materiality that is sometimes post-treated with coating and colouring for aesthetical or informative purposes. Post-treatments must be performed according to the RP technique to obtain a finished model. Treatments can include: de-powdering the model (3D print, STL), removing a support structure (FDM, MJM, SLA, LOM), UV light curing (MJM) and surface treatments like spray painting and application of coating material to increase material strength.

12

Including epoxy-based resins, optically clear resin, flexible rubber-like materials, thermoplastics, ABS plastics, polycarbonates,

polyphenylsulfones in different blends, colours and translucencies, polycaprolactone and acrylic photopolymer.

13

FDM is an additive fabrication method that uses a plastic filament unwound from a coil to supply material to an extrusion

nozzle which can turn the flow on and off. The controlled extrusion head deposits very thin beads of material onto the build platform to form the first layer. The platform is maintained at a lower temperature, so that the thermoplastic hardens quickly. No post-curing is required and the FDM technique also enables the designer to create functional snap-fit parts without any need for secondary processing. After the platform lowers, the extrusion head deposits a second layer upon the first. Supports are built along the way, fastened to the part either with a second, weaker material or with a perforated junction. FDM machines are produced by Stratasys Inc. (2011) or pp3dp (2011) 14

Up to the present a broad variety of RP technologies have appeared that were alternating established technologies by the

material or the curing mechanism. Most of these technologies received their individual Acronym but can be pinpointed to core technologies as e.g. sintering and 3D printing. The history of RP technology is at the same time also a history of failed attempts.

Terry Wohlers, an RP consultant and author of the “Wohler’s Report�, the standard reference manual for the industry has monitored the business movements and failures over last decades (Wohlers 1996-2011).

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

Rapid prototyping in architectural practice In architectural practice Rapid Prototyping technologies are classically employed to materialize designs in model scale and are chosen for accuracy, fast production and increasingly competitive prices. Contemporary digital designs demand sophisticated tools for their materialisation even on the model level and have undergone increasing proliferation through RP processes (Peters and de Kestelier 2008), (Adeyeye et al. 2006). The application of Rapid Prototyping is less an option than a necessity to cope with the faster design cycles and increased geometric complexity that can be achieved with contemporary digital design tools.

The print-out usually serves as a haptic interface for personal evaluation of the design’s qualities and promotes further formal three-dimensional studies (M. Burry et al. 2001, 4). RP models have also been used for the threedimensional visualisation of the analytical performance or GIZ data (Rase 2009) and been employed for functional testing used by wind engineering (Nadooshan, Daneshmand and Aghanaj 2007), environmental air quality and noise management. What we can witness in this area is a growing shift from a purely representative to a more explorative approach of model-building with the help of RP. RP models have also been applied widely in architectural academic training and are a vital part of the digital design curriculum (M. Burry 1998).

“RP can potentially support a comprehensive and integrated environment to study form, space making and the physics of materials relative to machine processes in construction.” (Sass and Oxman 2005).

The models are used in early design stages to visually examine parametrically generated form variations and later for prototyping fabrication tests. The technology is valuable for its potential to be employed in scaled-down versions of building and manufacturing processes that require an understanding of the construction sequence and fabrication constraints.

“The connection to materials for either design or construction quickly builds skill sets for rule-based design from the relationship between materials, modelled geometry and machinery. The characteristics of working with a particular material with RP machinery link cognitive design skills to modelling geometries.” (Sass and Oxman 2005) RP models can be fabricated by external service providers15 that specialize in CAM technologies, or by web-based platforms16 that offer a multitude of materials and print processes at a competitive price. More economical processes as FDM, 3D print, smaller SLA or the FAB@Home DIY printers see increasing application in architectural and design offices and educational institutions as an extension to the conventional workshop equipment and as an experimental design tool.

Several factors influence the financial volume needed for the acquisition, maintenance and production of RP technology.

-

Machine price

-

Material price

-

Print price based on geometrical constraints and modelling parameters

-

Material properties

15

E.g. Materialise NV (2011)

16

E.g. Shapeways (2011) 32

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

The more expensive technologies like SLA and SLS offer complex material properties whose performance and application are superior to the more primitive models generated in a 3D printing process. Current prices for high-end RP machines range from $180,000 to $500,000 for SLA, or $270,000 to $325,000 for SLS. The lower end of the RP printing technology product starts with machines as the V-Flash System for around $10,000 (3D Systems Inc. 2011). The most economical RP machine is the newly developed 3D printer by the Vienna University of Technology (Stadlmann 2011), which operates with light-hardened resins and can be acquired for the prize of $1750. Further low-cost printing devices are the self-assembly kit for a single-syringe printer by FAB@Home for $3025 (FAB@Home 2011) and the Personal Portable Printer for (pp3dp 2011) for $2890. All of these economical fabrication technologies operate with a single material in limited formats.

Application of Rapid Prototyping in the thesis The research conducted here employs rapid prototyping models as an investigative method to test the functionality of the design process and outline geometric constraints. Geometric differentiation can be tested with more economic Rapid Prototyping processes which then can be projected onto larger and more expensive Rapid Manufacturing tools. Printed colour maps created with the Zcorp printer equipped with colour cartridges can be coupled with physical prototypes to show the coherence between performance graphs and geometric morphology, serving as a fast and affordable measure to ensure the viability of the investigated process.

1.1.3 Application of Additive Fabrication II- Rapid Manufacturing (RM) Rapid manufacturing describes additive processes that create fully functional objects. This aspect develops a perspective on the object that goes beyond a purely scaled-down and representative materialisation of a design intent to produce a final artefact that can also be integrated into larger assemblies. Hopkinson, Hague and Dickinson provide the standard definition for Rapid Manufacturing that will be utilized throughout this thesis: “Rapid manufacturing is defined as the use of a computer aided design (CAD) based automated additive fabrication process to construct parts that are used directly as finished products or components” (Hopkinson, Hague and Dickens 2006, 1).

Rapid Manufacturing17 fabricates geometrically fully functional complex, low-volume or customised parts. The available materials incorporate plastics, metals, alloys and ceramics among others and allow manufacturing to be decentralised to produce parts more quickly, less expensively and with greater flexibility.

Rapid Manufacturing started with functional SLS processes in the late 1980s that were expanded by Laser Engineered Net Shaping (LENS) (MacCay 1995) and related processes that could deliver full-density components in a variety of metals. The controllable hardening of metallic powder used high power Solid State Lasers and electron beams whose functionality was already known from the earlier research on Ruby laser systems conducted by Theodor Maiman in the early 1960s (Maiman 1961). In the following years several new materials were developed for RM processes, such as high-elongation and flameretardant materials, further expanding the application of the process beyond the previously mentioned fields.

Contemporary RM allows digital fabrication with the following build materials (selection): -

Metals: stainless steel, titanium, tool steel, alloys of titanium, aluminium, cobalt and nickel, nickel-based superalloys, nitinol

17

Biological materials: hydrogel (agar, gelatin, collagen, fibrin)

RM is also referred as “direct manufacturing”, “direct fabrication” and “digital manufacturing”.

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

-

Prosthetic materials: ceramic paste, melting thermoplastic polymers, polymer-coated calcium phosphate, polyurethane

-

Nanomaterials: nanotube + nickel, nylon and nanocomposites

-

Ultra-clear polymers with optical properties18

-

Polymers

The broad bandwidth of materials, increasing build sizes and proliferation of computational design tools promoted application of these technologies in many industries. Rapid manufacturing already has been successfully integrated in many fields.

-For aeronautical applications in gas turbine swirlers (EOS GmbH 2006) and complex airplane ductwork (Vashishtha, Makade and Mehla 2011, 2492) among others.

- For the layered manufacturing of food (Periard et al. 2007) - In industrial design for, e.g., jewelry and textiles (Hopkinson, Hague and Dickens 2006, 276-281).

- In defense applications: The Mobile Parts Hospital (MPH), a mobile fabrication unit of the US Army, equipped with additive and subtractive tools, provides replacement parts not “readily available elsewhere, including bolts, brass studs, and pulleys” (Craig 2005, 16) in conflict zones.

- The medical sector applies RM processes for functional prosthesis manufacturing (Koo et al. 2005) and reconstructive surgery of kneecaps and hip joints, facial reconstruction (Kai et al. 2000) that implements geometric customisation of the fabricated model based on collected 3D computerised tomography (CT) and magnetic resonance imaging (MRI) data.

A critical aspect in such operations is the acceptance of the replacement parts, mostly hip or knee joints, by the existing living tissue. Recent research by Pompea et al. (2003, 45) investigate a graded layering of biodegradable polymers, which delivers an additively fabricated scaffolding for the allocation of titanium and ultra-high-molecular-weight polyethylene (UHMWPE) joint material, providing for better mechanical performance of the implant and reduced rejection by the neighbouring tissue.

- Further medical applications of Rapid Manufacturing can be seen in additively fabricated biodegradable lattice structures with controlled architecture of hierarchical porosity, which helps the affected body part in many parallel functions by providing controlled cell nutrition, mechanical support, permeability and functional elastics.

Contemporary research has successfully employed and tested a broad range of these materials for the creation of such implanted structures. Hollister writes: “SFF [Solid Freeform fabrication] has allowed fabrication of scaffolds with controlled architecture from polymer, hydrogel, ceramic and even metal biomaterials.” (Hollister 2005, 522)

Rapid Manufacturing in architectural practice The last years saw several research processes investigating the implementation of rapid manufacturing into architectural workflows. Although similar in their objective to create fully functional building parts or even entire buildings, the processes differ significantly in their tectonics, materials employed, geometric constraints and achievable complexity of the final artefacts. The additive fabrication of larger building elements points to interesting and far-reaching advantages over a conventional manufacturing process of standardised discrete elements assembled in a controlled time sequence, but is still in an early development stage.

18

Optical properties in this context refer to translucency and not a true optical quality that would allow the additive fabrication of

lenses etc. In this sense the term, promoted by the company, is misleading (DSM Somos 2011).

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Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

One potential application for such mega-scale additive fabrication of building components in actual size lies in the manufacturing of morphologies optimised in terms of form and topology,19 which still pose challenges to conventional subtractive methods due to the complex geometries that emerge from the form-finding process. Since additive fabrication processes allow the creation of geometrically complex objects in the same amount of time as regular shapes, these challenging forms become achievable if they comply with the given manufacturing standards of the individual technologies with regard to minimum material thicknesses, build sizes and geometric modelling.

The fabrication technologies on a building scale can be sub-divided into manufacturing processes with or without support structure materials to stabilise overhanging geometries. This aspect has profound consequences on the geometrical boundary conditions and the fabrication of such as will be explained in the following.

Mega-scale additive fabrication without integrated support structure Main research on the first aspect has been conducted by Behrokh Khoshnevis, who developed the “Contour Crafting” process. The envisioned process releases slurry composed of fluid build material (usually concrete, but ceramics including piezo-electric actuators have also been researched) from a nozzle in a layered fashion, whereby the lateral elevation of the material deposited by tube is controlled by a pair of robotically guided trowels that shapes the contour of the emerging form and delivers smooth surface finishing. Khoshnevis envisions a complete robotically controlled building process that can be achieved in such a manner, including automated distribution of steel reinforcements, electrical wiring, piping and automated tiling distributions for interior finishes (Khoshnevis 2004). For the creation of overhanging vault-like structures he applies a building sequence similar to the adobe masonry process, which materializes curved shapes by a coupling a different brick distribution sequence to approximate the desired course.

Ill. 1 Left: contour crafting of a barrel vault structure, right: adobe masonry distribution of bricks (Khoshnevis 2004, 9)

From the proposed system, extruded shapes appear best suited to avoid the computation of complex build sequences in accordance with the desired stability during the build process.

The architectural applications of such a layered building system are promising—according to Khoshnevis—in the construction of buildings that require a fast building process, like emergency shelters and low-income housing.

Further studies are under way to investigate applications for lunar and Martian construction projects that could utilise local planetary soil as a build material. Considering the complexity of the process, an application for erecting 19

See here Li and Chen (2010), Hiller and Lipson (2009).

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economical low-income structures appears critical, since the technology has to compete with well-established construction systems that allow the fabrication of houses with wooden balloon frames or similar structural systems.

Utilisation under emergency situations, like after hurricane Katrina or the Asian tsunami, appears unrealistic due to the amount of electricity required and conditions needed for the erection, transport and operation of the required devices.

A similar investigation on the layered distribution of cement-bonded mortar for building components is being conducted at the Concrete Printing research group of Lorborough University’s Civil and Building Engineering department. During the fabrication process a nozzle ejects a build material in a freeform planar course based on layered information retrieved from a 3D model. In contrast to the contour crafting process, no additional formgiving animated trowels are used. Conducted research is restricted to building components and includes research on integrated voids for steel reinforcement and the technical supply of additional building functions (Ill. 2).

Ill. 2 Building component fabricated by the Concrete Printing Group at Lorborough University (arbitare 2010)

The envisioned scale of the thus created artefacts does not attempt to additively fabricate entire building structures, but rather to manufacture customisable building components of extruded geometry.

Although both processes utilise a sequential layered assembly of material, the geometric freedom that is usually associated with additive fabrication processes cannot be exploited in full because the lack of support structure material that stabilises overhanging geometries becomes critical. This limitation constrains the degree of complexity achievable and allows only certain volumetric designs to be produced. Under these boundary conditions it is questionable whether the benefits of additive fabrication technology with regard to local detail and achievable complexity can be fully perceived since significant fabrication constraints must be implemented even during the digital modelling process. The presented technologies therefore have to put themselves in direct comparison to established fabrication technologies like the in-situ casting of concrete, which would allow the fabrication of similar components with more precision and potentially higher complexity as regards shape and surface textures. In the classical concrete casting process the milled cast would serve as the support structure for overhanging geometries and therefore allow the production of even fully double-curved objects.

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Mega-scale additive fabrication with integrated support structure Until now only one mega-scale additive fabrication procedure exists that contains a build-in support structure. In 2006 Enrico Dini began developing a process that he coined “D-shape printing” (Dini 2010). In his method, which in principle resembles a Zcorp plaster print process, a distributed powder bed consisting of ground natural stones and metallic fibres is hardened locally with an ecologically friendly resin. During the build process an array of parallel valves that eject the binder fluid migrates over the powder bed and releases the binding agent according to the perimeter information retrieved from the digital model. In the first two processes the actual build material was released from the valve, requiring a high degree of structural stability that would be achieved by limiting the geometric envelope in which the process was feasible. In this process only the binding agent is released on a planar powder bed that leads to local hardening of the geometry’s perimeter. Unbound parts of the powder-bed nevertheless serve to stabilise the surrounding geometry and can be removed mechanically once the print process has been completed. The entire structure is then built through a layer-by-layer distribution of the powdered material in thicknesses between 5-10 mm, depending on the expected accuracy of the final component. The material properties achieved through such a process resemble those of light concrete and yield a rigid and robust haptic appearance.

Applications of this process have centred mainly on the production of artworks and initial full-scale tests of small buildings and sculptures. Further investigations have been also conducted for the production of lunar dwellings through an additive fabrication system that utilises local soil (Ceccanti et al. 2010). Advantageous for such an endeavour is the reduced amount of water necessary to create (supporting) structures that have to be removed once the system has been erected. The current state of development allows the production in a building chamber structure 600 x 600 x 600cm in size, yet a full model in these dimensions has not been accomplished yet. Existing objects are usually composed of a segmented construction of individually produced smaller parts that are assembled after the production has been completed.

Research is currently being conducted by James Gardiner (Gardiner 2009) for the design of a villa in Sardinia that is fully constructed from assembled elements. In Ill. 3 shown below, this segmented approach is apparent in the fabrication of a column element. The design contains material voids to reduce the self-weight of elements created in this way and shows circular cavities for the allocation of tensile rods that are required to assemble the components on site. In the example shown overhanging geometric parts in the hollow core of the column can be traced that would not be feasible as such with the additive fabrication systems mentioned above.

Ill. 3 Left: “Parametric column 1” (Gardiner 2009), right: sections of “Parametric column 1” printed with D-shape technology

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The D-shape process appears to be the only method that transports the full benefits associated with small-scale additive manufacturing processes to a larger scale, yet further work and studies have to be performed before it can achieve potential application in a more straightforward architectural project. The process that builds upon fine granular stone material, small valves and a binding solution poses challenges to the quality control of the build process since the valves must be kept clean at all times to ensure consistent structural properties of the printed object.

All of the mega-scale additive fabrication processes mentioned show traces of their production process through visible grooves indicating the thickness of the deposited material. Mega-scale additive fabrication suited for the building site requires further studies in appropriate materials, implementation of structural reinforcement, long-term investigations of mechanical properties in different interior and exterior environments, and a design process that has to tightly connect architectural formgiving, structural analysis and fabrication constraints.

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Excursus: Mega-scale additive fabrication of a compression-only vault structure The author and Ricardo Gomes have used the D-shape process to design and fabricate a vaulted structure (Ill. 4), employing a form-finding tool developed by Philippe Block for the creation of compression masonry vaults. The chosen structural application that operates as a plug-in for the Rhino 3D modelling program was “[b]ased on the Thrust Network Approach (TNA), which uses a force network as discretization of the shape, [and allows] to internally redistribute forces within the network using force diagrams.” (Block, Lachauer and Rippmann 2011).20 In the formfinding process, user-defined line grids that circumscribe the footprint of the later design undergo iterative calculations until a structural equilibrium of pure compression forces is created and represented by a threedimensional formation of the initial line network. Besides the generated three-dimensional structures, a twodimensional graphical statics diagram is generated that maps the forces present within the discrete line elements at the specific optimisation step. These diagrammatic values can be used to define the later piping diameters that react to forces by expanding and contracting in their given directions. This spatial network of intersecting lines is usually translated into boundary curves for the creation of masonry shell surfaces that can be fabricated by methods like, e.g. the Catalan vault technique, as shown in (Block, Ochsendorfer et al. 2008). The optimisation goal of the Thrust Network Approach corresponds well to the load-bearing capabilities of the natural stone granulate used in the Dshape process, which operates well under stress and has only limited strain-bearing strength. In the case presented here the generated force lines were piped with a diameter of 4 cm and used to create a quasi-gridshell structure in full-size dimensions (height 2.00m x width 1.00m x depth 1.00). In the developed design a wall structure—visible around the columns–migrated subtly into a gridshell. The printing processes operated with a layer thickness of 5mm and produced tubular diameters increasing to up to ca. 5.0 cm (Ill. 5 ) in the final model due to the processural reaction between binder and granulate. During fabrication the ejected binder is absorbed by the print material and responsible for slight geometric irregularities and structural expansions in comparison to the original digitally sectioned printing area. The printed vault was equipped with a base and a sideplate that were added to the digital design and allowed damage-free erection and transport after the finalisation of the printing. In the finished model the base-plate was kept to allow transport in an upright position.

20 The text will not expand on this form-finding process, but further information can be found in Philippe Block’s dissertation (P. Block 2009), which reveals the full technological background and shows suitable applications of this process.

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Ill. 4 Left: digital model of a vaulted structure, right: materialised D-shape model

Ill. 5 –Left: D-shape print of vaulted structure before depowdering, right: top detail

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Rapid Manufacturing and quality control measures Similar to smaller scale rapid manufacturing processes, quality control-related issues pose a further obstacle to broader implementation in the building market. A persistent structural quality that can be expected from large-scale printed artefacts requires a more matured and tested additive fabrication technology. Once this has been achieved this sector can be integrated into existing processes of standardisation and quality control.

The last two years saw increasing efforts in those areas that inspected the terminology, materials and processes and were driven by the American Society of Manufacturing Engineers (Society of Manufacturing Engineers 2010) and the ASTM Standards Committee F42 (ASTM International 2010) on Additive Manufacturing Technologies.21 In the case of a qualitative classification of the material properties that can be produced with additive fabrication— especially for metals and their alloys—broader implementation can be expected that would not rely on the quality testing of individually produced artefacts, but rather operate according to a technology-specific standard. These adjustments allow larger-scale implementation of additively manufactured components in production processes since expenses that were initially reserved for quality control measurements could then be partially eliminated. Under such circumstances a stronger development from the manufacturing industry could be expected that would eventually lead to enhanced fabrication processes The issues still pending concern analysis, manufacturing and material development to ensure the predictability of the artefact’s quality independent of its manufacturing circumstances. For a successful realisation of structures and components in varying scales, a standardised material description, testing procedures and analysis methods have to be developed in the coming years that take into account the local machine specifications as e.g. build direction or machine properties. This is especially relevant for implementation into a building practice in which the elements experience longer life spans.

Property testing of these complex spatial structures is a challenging task, since it ideally requires two-level analysis. A primary analysis of the print material’s structural properties has to be coupled with an examination that takes into account additive fabrication parameters like the local scale, build direction and layer thickness. These fabrication properties can have significant effects on the structural soundness of the artefacts. Several build material suppliers already differentiate their material properties according to the build axis.

1.1.4 Application of additive fabrication III: Rapid Tooling (RT) In the first five years after the introduction of rapid prototyping, the focus of additive fabrication centred on the creation of representative materialisations of digital designs through abstracted models with limited functionality and material performance. With the arrival of rapid tooling processes used for the creation of casting patterns, such as Direct Shell Production (DSPC) (Sachs et al. 1993) the models became a generic physical component in an actual industrial workflow and opened the application up to rapid manufacturing.22 The text touches on this specific application of additive fabrication only briefly since its use is centred mostly on the high-quantity output of industrial products and sees no application within architecture. Advantageous for the application of additive fabrication processes is the short time span between design development and functional testing required in certain industrial fields like automotive and consumer electronics. Since the products created in 21

See also EOS GmbH/Deutsche Industrie Norm (2010).

For more detailed insight into rapid tooling processes, manufacturers and applications, see Chua, Leong and Lim (2003, 231263).

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this way have to comply with the parameters of the casting process itself, geometric limitations remain. The controlled accessibility of the casting material presents an obstacle to certain geometric forms that can compromise the structural properties and quality of the product. As this research strives to investigate production properties that fully benefit from the novel properties of additive fabrication, procedures that have to compromise this quality are not dealt with in depth. It is the belief of the author that a successful integration of additive fabrication processes can be best achieved through a focus on these properties that do not compete directly with well-established fabrication processes, but have to identify, conceptualise, produce and analyse their own typology of applications that expand the given scope of production.

In rapid tooling processes the ceramic mould is built in layers by slicing the digital model into cross-sections with a given layer thickness, spreading a fine layer of aluminium powder with a roller mechanism, and depositing a liquid resinous binder in regions corresponding to the cross-section of the mould with a multi-jet print head moving across the section. This process is repeated for each layer until the entire mould is built. The binder deposited for each layer penetrates the pores between the powder particles, resulting in the layers adhering to each other. The mould can contain an integral ceramic core in order to produce a hollow metal part. Once the mould is built, the excess powder is cleaned away and the mould is fired. Rapid Tooling is used for the production of functional moulds, mould inserts and tools.

Two principles are employed in Rapid Tooling:

Direct Tooling In direct tooling the additive fabrication process delivers the tooling directly. Direct Tooling technologies include Direct Metal Deposition (DMD), Laser Engineered Net Shaping (LENS) and ACES (accurate clear epoxy solid).

Usually the mould inserts created with this method have to be post-processed to guarantee near net shape product accuracy and is usually achieved by milling off surplus material and polishing the final product to ensure a highquality casting process.

Indirect method In the indirect method additive fabrication processes are used to generate a pattern from which the tooling inserts are made.

For a silicone rubber moulding a stereolithographic or selective laser-sintered pattern is used as a male pattern for the creation of a mould. The master pattern is fitted with a sprue and gate and then surrounded by a parting surface which establishes the parting line for the mould, required for the removal of the final tool. The assembly is mounted in a vat and liquid vulcanisation is then poured over the pattern and parting surface combination. The detailing depends on the RP male model and the viscosity of the mould material. In a next step the RP model is removed by separating the two moulded halves, and the casting pattern is ready for production. The finished patterns have to be post-processed to comply with industry tolerances and surface finishes. The removal of the stair-stepping effect of the volume along the build direction inherent in additive fabrication is usually accomplished by milling to achieve the net shape form of the final mould.

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1.1.5 Summary Additive fabrication processes create new manufacturing and design potentials for many disciplines. These are based on the following three innovative technological characteristics: •

The generation of data is inherently based on a sliced process of 3D information; the resulting

production tolerances that can be achieved remain invariant to the complexity of the sliced object. •

The manufacturing constraints are significantly lower and allow the production of geometrically

complex objects that are impossible to realise with conventional manufacturing processes such as interlocking geometries with local variation. •

The creation of data is based on CAD tools. The outcome of additive fabrication is therefore

closely connected to the abilities of the software packages employed. Developments in computational design can be inherited and readily integrated into novel printable artefacts if they comply with the discussed boundary conditions of additive fabrication.

These properties define the innovative conditions for design and manufacturing processes devised using these methods and differentiate additive from subtractive fabrication. It is estimated that they will persist in future developments within additive fabrication on all scales and be critical for the emergence of derived design and production processes up to an architectural dimension. Despite the obvious challenges faced by the technology with regard to material properties and economic boundary conditions, further exacerbated by a lack of persistent quality regulating standards, an architectural investigation can nevertheless be undertaken. The arrival of additively fabricated building elements for permanent installation on site in a notable quantities is probably decades ahead, yet the fabrication tectonics from which these elements will be constructed can already be investigated today with reasonable accuracy. The preparation of a broad spectrum of research knowledge on dependent design procedures, computational material specification and applicability in an architectural context will be rewarding once the technological boundary conditions are ready for permanent structures. The submitted thesis is a first step in that research direction and will require the continuous application of its abstracted findings to technological developments and their architectural consequences in the future, undertaken by academic institutions and industry.

The analysis of these generic process conditions and the extraction of its most challenging aspects can now serve to outline the research questions and their respective hypotheses, which are posed in the following chapter.

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Research Questions I-III and Hypotheses I-III

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2.0 Introduction Additive fabrication’s ability to create digital content geometrically with irregular and local variation of its described volumetric entities represents a core contribution to the manufacturing methods available today. Since the technology allows the fabrication of complex parts regardless of their detail in the same amount of time as simpler geometries, its use in digitally driven design has been widespread.

Additive fabrication technologies can gain importance in future production pipelines through a focus on the inherent benefits associated with the technology, rather than in an attempt to compete with tried-and-true manufacturing methods such as vacuum forming, milling, casting and moulding. The inroads into a fully integrated manufacturing practice will be constructed by concentrating on solutions that are unsolvable in other technologies. The recent technological developments improving the possible material quality, geometric control and build sizes of additive fabrication open up manufacturing and computational possibilities that make it far more than “just another production method�. It is claimed that the technology could be used increasingly to specify the designed object locally beyond the benefits of accuracy, speed and achievable complexity already associated with additive fabrication.

The technological developments described point to a new research field that employs the technology to produce its own specific class of materials. The objective is to develop digitally controlled structural and material systems with local variations that are complicated or impossible to create with conventional manufacturing technologies, and hereby pave the way for an innovative and meaningful contribution to the manufacturing spectrum. It can be claimed that the creation of a digitally defined, fully functioning, three-dimensionally heterogeneous material typology can benefit especially from the inherent advantages of a computer-guided and computer-generated additive fabrication process. These future materials will implement layers of material and structure-related performance information to configure their projected behaviour, independent from the geometric complexity of the modelled structure. These tuned structures exhibit a set of unique properties that are not usually present in conventional materials and are essentially synthetic. CAD tools can allow a selective configuration of such material composition orchestrated by a set of external data. These transitive, three-dimensionally heterogeneous mechanical, structural and functional properties can then be investigated for the design of future innovative architectural components.

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2.1 Research Question I Heterogeneous mechanical properties through structural control of material properties The first research question will centre on a process combining digital design tools and individual material additive fabrication processes to develop a structurally calibrated material with inscribed dynamic properties. The existing research void in this area can be traced in the literature review that follows this chapter. Research on additively fabricated material design with heterogeneous properties can build upon existing research from the fields of material research and structural mechanics and inform the implementation of the computational model and the applied testing schemes.

2.1.1 Digital control and variation of discrete elements through topological rulesets Inherent in the digital modelling process that precedes additive fabrication is the ability to digitally control volumetric information that serves as the basis for the later slicing and printing process. The first generation of architectural and engineering drawing programs were basically “a digital translation of the known drawing tools with the mouse and screen replacing the pencil and paper� (Terrien 2005). In the last ten years digital modelling tools have been expanded significantly and allow finer tuning of the respective geometric content. Discrete geometric entities are not altered individually, but integrated into a relational or evolutionary system of user-defined conditions through which a form is constrained. In current modelling applications these behavioural rules are set to encode the specific geometric performance and can be driven by data retrieved from various external sources. Software development in the areas of building and structural simulation thus allow for feedback cycles between computational modelling under optimisation criteria that are reflected in the locally varied geometric morphologies of the discrete parametrically defined elements.23 This control over discrete variable geometric entities organised in a systematic manner and the fabrication of such, points to a research field that merges digital design and additive fabrication and can be utilised to fabricate structurally differentiated material properties that have not yet been investigated in full.

2.1.2 Correlating digital design and fabrication for a tunable material design The digital design of materials with adaptable and changing structural composition in a singular materiality appears to be an especially rewarding subject, since locally varied geometries can be digitally controlled and fabricated in the same amount of time as regular three-dimensional structures. The materials created in this way can be designed such that an active material performance can be calibrated digitally and thus further expand the scope of available materials. Contemporary state-of-the-art additive fabrication technologies allow the production of experimental specimens in dimensions sufficient to allow proper testing as fully functioning prototypes.

2.1.3 Parameterising natural structures Natural structures like foam, wood or cancellous bone show local variations in their periodically arrayed cells that are often correlated to an aspired performance the material has to deliver. Foams obey a clear mathematical ruleset that defines a dense spatial packing of its discrete describable geometric entities. The internal composition of wood and cancellous bone cells adapt their spatial extension to external mechanical requirements and develop a structurally and materially optimised periodic substructure that guarantees efficient performance and low self-weight even under dynamic load conditions. Material research provides parameterisations of these three-dimensional structural sub23

Further implications of these processes on the architectural design process and how they relate to additive fabrication will be

discussed in the section 4.3.2 Digital design and material performance.

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elements upon which this research can build (see here Gibson and Ashby 1988, Weaire 1997, R. Lakes 1993, R. S. Lakes 1987) and translate into digital modelling processes.

Geometric models that can be created and additively fabricated in such a fashion consist of a three-dimensional cellular array of discrete topologically invariant elements and external performance information that calibrates the local morphology.

2.1.4 Material and mechanical complexity Direct control over the material’s mechanical behaviour can inform the architectural design process and lead to a new dialogue between materiality that actively implements these properties to achieve the desired purpose. The perspective on the employed material is hereby not a static one but has inscribed performance potentials that can be designed by the architect. Traditional manufacturing methods for such dynamic structures are usually connected to a series of mechanically interconnected and hydraulically driven elements orchestrated with respect to an envisioned movement profile. The controlled material properties can be activated by more simple mechanical tools with additive fabrication, since the performative complexity would be embedded in the material structure, but would nevertheless provide for comparable performance by the element. The research therefore will identify suitable structural building blocks that illustrate this distinct form-changing aspect in all three dimensions in the experimental studies.

2.1.5 Relevance The research could develop digital tools that allow the local calibration of material properties through their structural composition. This novel design process could expand the existing selection of available fabrication materials by adding a new type with controllable properties that would allow a correspondence between the structural or performative profile of the designed object and the materialisation of such. The computational encoding of material structures designed through cellular elements with topologically invariant properties can be applied to changing additive fabrication technologies since the scale can be adapted to changing geometric boundary conditions. The spatial distribution of these elements nevertheless must be aligned with the fabrication scale, since this affects the self-weight and thus the buckling/bending behaviour of the final structure.

The thesis will therefore formulate the first research question on the creation of digitally defined materials with tunable properties based on structural variation in composition as follows: Can additive fabrication be employed for the rapid manufacturing of cellular materials with tunable properties based on digitally calibrated structural variation?

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2.2 Hypothesis I -

The research claims that the properties of additive fabrication and computational design can be coupled to define a new type of synthetic singular material with gradual mechanical properties through variations in its substructure.

-

The research claims that related research from the field of material science, especially on the parameterisation of structural solids, can be implemented in accordance with the boundary conditions of the digitally driven process. The research plans to utilise matured additive fabrication technologies using a singular material to achieve the research task.

-

The research claims that the control over the properties of such a material can lead to novel possibilities for architectural applications since individual mechanical performances can be integrated into each element of the structure. These properties can affect inscribed form-changing potentials or provide for a gradual flexibility that is achieved locally by controlling the material’s structural composition.

-

The research hereby utilises the innovative properties of additive manufacturing and the latest digital design tools to construct a material with high amounts of local geometric variation that cannot be achieved with conventional fabrication procedures.

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2.3 Research Question II Additively fabricated three-dimensional composite structures with graded mechanical properties The second research question focuses on recent technological developments in additive fabrication for the creation of multi-material composites.

2.3.1 Multi-material additive fabrication The multi-material additive fabrication process by Objet Geometries (Objet Geometries Ltd. 2010), introduced in 2007, allows the materialisation of objects with up to 14 predefined materials. This development adds a wider material choice to the fabrication process while taking full advantage of its intensive properties. It is estimated that the existing technology will proliferate in the future through better and more durable material properties on larger scales, but preparatory research can already be conducted today that allows its adaptation to the changing technological conditions of the future. Since the thesis investigates an application of additive fabrication for rapid manufacturing purposes, a research objective must be defined that goes beyond the existing representative model approach and expands its application accordingly.

The research question strives to employ this innovative additive fabrication technology to create a digital composite material with tunable properties. Here, again, the thesis can build on existing research from material science that has developed manufacturing and simulation tools for the creation of material with graded properties in two dimensions.

The studies presented here allow the thesis to examine the utilisation of additive fabrication procedures for the creation of a digital materiality from two distinct perspectives. The first experiment attempts to create tunable mechanical properties by locally altering the structure of its discrete cells, whereas the second experiment—described here—would develop a goal-based allocation of different materials with varying properties using periodically arrayed geometries. The specimens developed experimentally highlight the unique advantages of additive fabrication that could not be achieved through other manufacturing processes.

2.3.2 Implementation of existing research on functionally graded material The digital control and manufacturing of objects constructed of multiple materials—usually two—has been investigated in the past in the field of functionally graded materials (FGM), which studied the control over the structural compositions of metallic material pairs in two dimensions. Materials created with locally differentiated material properties would thus allow functional differentiation by calibrating the structural composition within a single object. A transfer of this knowledge appears rewarding for a novel application of the multi-material additive fabrication process described above. Similar to the pair of metallic materials described, the 14 polymeric structures employed in the Connex differ in terms of their mechanical properties. The integration of these properties in a design process of additively fabricated materials allows the calibration of a composite material of gradual heterogeneous mechanical quality in all three dimensions.

2.3.3 Finite modelling processes as a design tool The study requires a digital design process that defines the local assignment of different digital materials in accordance with their desired performance profile. At this point in time no specific software is available that can fulfil this purpose per se. In order to achieve this task, existing tools must be surveyed and modified in function.

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Mature solutions in the field of structural simulation, using the Finite Element Method (FEM), can be studied for this purpose.

In these applications material properties can be determined and a load case scenario defined that incorporates applied forces and bearings. The numerical process sub-divides, or “discretises�, a given volume into geometrical sub-components such as bricks or tetrahedrons and applies a partial differential equation under the given boundary conditions. The accuracy of the method depends on the sub-division ratio of the geometric object in question. Finer sub-division produces more precise results but requires longer calculation processes. In the calculation process local deformation values of iso- or anisotropic materials can be extracted and analysed.

In theory this process could be used in a reversed fashion as a design tool to allocate the selected material that is brought in compliance with the desired deformation behaviour. The resulting material would correspond with the FEM model in terms of its sub-division, and consist of a three-dimensional periodic array of elements with differing mechanical properties that could be realised through the volumetric assignment of geometries with individual materiality. The research aims to investigate the application of this digital method to derive a functioning threedimensional sorting method to allow the allocation of the six available materials to the appropriate locations within the test object.

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2.3.4 Relevance The research conducted here can provide a novel method for correlating structural behaviour to a heterogeneous material composition that can be realised only through additive fabrication technologies. This material design method should allow heterogeneous mechanical properties to be implemented through a digitally driven sorting process of three-dimensional material distribution that implements finite element methods in a novel manner.

The thesis therefore formulates the second research question on the creation of digitally defined materials with tunable properties based on material variation within a periodic substructure as follows: Can additive fabrication be employed for the rapid manufacturing of cellular materials with tunable properties based on digitally calibrated material variation?

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2.4 Hypothesis II - The research claims that multi-material additive fabrication processes can be used for the creation of a digitally defined heterogeneous materiality in three dimensions through variation in its material composition within its internal periodic substructure.

- The research claims that FEM-based processes can be applied to define the distribution of the different materials within a digital model that can be fabricated accordingly.

- The research claims that existing research in the field of material science and structural mechanics, especially the field of Functionally Graded Materials, can be integrated to benefit the development of such a process.

- The research claims that a correlation between the desired structural performance scenario and material composition can be achieved through local control over the material’s mechanical properties.

- The research claims that the planned design and fabrication of a heterogeneous material utilises the special intensive properties of multi-material fabrication processes for the creation of a material that can only be materialised in such a manner.

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2.5 Research Question III Design implications of additively fabricated heterogeneous materials The proposed control of a tunable material performance through additive fabrication technologies and multiple digital tools affects the design process in many areas and constitutes a research field that has not been explored thoroughly. The research question proposed here investigates the following topics: a.

The impact of actively integrating materials with geometrically and mechanically controllable composition that expands the traditional conception of materials with known properties must be examined with regard to its conceptual implications for the role of the designer and the design.

b. The coupling of digital design and material performance requires new interfaces and digital workflows that can implement a wide scope of external driving factors. The translation of multiple digital resources, individually or in an orchestrated fashion, into a dynamic digital model that drives the fabrication information of distinctive new structural typologies alters a traditional design process and is ripe for investigation even today.

2.5.1 Mirroring historical and contemporary architectural design processes Integrating material performance in a systematic digital workflow and fabrication pipeline extends the existing architectural design process and shows analogies to geometric developments in the Renaissance. With the introduction of projective geometry in the 16th century, initially for visualisation purposes and later as an integrated architectural design and fabrication practice, the relationship between the designer and the designed was changed.

This geometric protocol that ended the dominance of Euclidian geometry introduced flexible variation of geometric content and connected these with the possibility of directly retrieving manufacturing information used for the specially formatted stereotomic drawings issued to the stonemasons within a single drawing format. This format included external formgiving elements like “law curves” that served as an abstracted interface, whose alteration was reflected in a change in the form of the designed object through a cascade of choreographed geometric operations like rotations, projections and mirroring (“rabattement”).

The apparent abstraction of a direct design process from the final and concrete object that this practice entails was achieved through external geometric constructions. This geometric protocol, which could also be used to retrieve fabrication information, broke with a classical Euclidian tradition of form description that was centred on the direct definition of measurable properties in a straightforward manner. A new typology of architectural elements (“trompes”) designed and fabricated with this innovative workflow emerged in later years. This historical analogy is mirrored in contemporary computational processes of digital design that are driven by abstracted interfaces with inscribed geometric and logical conditions that compute the final form and allow the direct extraction of manufacturing information from the digital model. This geometric process is now expanded by integrating a material performance that can be steered and fed back into the design process itself. The digital workflow of additive fabrication expands the existing design protocol and actively integrates physical performance in an artistically inspiring manner. This aspect points towards a design culture that conceptually assimilates a structural or material performance that is far from static.

Achieving a conceptual and technological understanding of these processes lies at the core of this investigative endeavour. This research actively integrates a historical perspective on architectural formgiving processes guided by 53

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

geometric protocols and their conceptual implications in an attempt to integrate recent developments within the respective fields into a tradition of architectural research and potentially extract insights that can be transferred to our day.

2.5.2 Textile logic and material performance In analogy to the Renaissance processes that established a new typology of architectural building elements, the presented correlation between the digital design and manufacturing of materials can pave the way for a new type of distinctive structures that can be informed by the previous experiments designed to investigate structural and composition control. These structures can establish a new tectonic language that promotes a dynamic and differentiated material performance and takes full advantage of the fabrication properties. The ability to exercise geometric control over local structural morphologies can be combined with a systematic tectonics that organises discrete elements in coherent fashion. The digital translation of textiles with their inherent structural logic thus appears to present a valuable research field to investigate such an emerging typology for several reasons: 1. Textiles have a structural logic composed of discrete elements that can be diagrammatically described and translated into digital tools and varying materiality.

2. Textiles vary their spatial extension in a distinct manner that is constrained but flexible and introduces a formal domain of possible states in which the morphology can appear. For textiles, form exists as actual and virtual potentials that grant a temporal identity driven by the multiplicities inscribed in the given material and structural tectonics.

3. The abstract structural logic of textile assemblies with homeomorphic properties allows synchronisation to multiple scales that can be adapted to the distinct additive fabrication technology.

2.5.3 Multi-level design processes Due to the topological quality of the applied digital design processes—apparent in the first two experimental studies—various conceptually relevant external sources can be integrated into the computational model and additively manufactured. These instances can be applied for artistic formgiving purposes, but can also follow a desired articulation of a dynamic performance within a given range that has a more functional rationale. This workflow grants the material a special role since the resulting performance goes beyond a stated preconception of design intent, especially for dynamic structures, interpreting the geometric boundary conditions in a material-specific manner that can inform a design process in a novel fashion. From a designer’s standpoint, different conceptual approaches can be integrated sequentially or individually as formgiving instances and negotiate their effects through the performance thus created and defined. This approach could grant the material performative complexity and broader artistic freedom within the workflow. Objects that are designed and fabricated in such a manner regain conceptual and physical autonomy as their coherence between form and desired function is grounded in the morphological transformation potential inherent in the material itself. Multi-level design processes that combine active material performance within a digital and analogue model can unfold conceptual, artistic and physical domains with “inexact yet rigorous” properties (Deleuze, Guattari and Massumi 2004, 405).

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2.5.4 Relevance Digital processes that actively integrate a material’s mechanical property as active components in an architectural design have just recently become the subject of academic research (see: ICD 2010, Knippers 2011, Tamke et al.

2011). This current of research inspects mostly classical building materials like wood and sheet metal, attempting to integrate their inherent structural mechanics in a novel digitally driven design process with active material performance.

A consequent understanding of digital materials with controlled mechanical properties and their respective role in a design process and building typology that can emerge this technology has yet to be explored in full (see: N. Oxman 2010, N. Oxman 2010, Hiller and Lipson 2009). Despite the contemporary limitations in the achievable scale and durability of these materials, this investigation can contribute—on the one hand—to the contemporary and historical dialogue on the role of material in the architectural design process and—on the other—foster a rapid implementation of these approaches in a matured additive fabrication technology once the pragmatic boundary conditions have adapted.

The thesis will therefore define the third research question that centres on the investigation of a new design protocol with multi-level design processes and distinctive typological properties of building elements created in this way: Can additive fabrication processes for tunable material composition and multi-level digital design create a new design protocol and characteristic tectonic typologies?

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2.6 Hypothesis III - The research claims that through the active implementation of material properties that can be modelled and additively fabricated, a novel design protocol can be achieved that is characterised by the integration of heterogeneous material performance as a design driver.

- The research claims that new characteristic tectonic typologies of the artefacts created in this way can be conceptualised that integrate those properties in an innovative fashion.

- The research claims that a broad variety of external input sources can be translated into the digital design process to generate and release a novel structural tectonic with heterogeneous dynamic properties.

- The research claims that the interpretation of historical analogies can be beneficial for an understanding of such contemporary approaches and enrich the contemporary discussion on the integration of material performance into a design process with standard and tunable materials.

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Methodology

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3.0 Introduction Additive fabrication technologies have been undergoing steep development cycles since their innovation in the late 1980s, allowing users to materialise unprecedented geometries of high detail and controlled local variation in ever more dimensions and applications.24 The deployment of digital processes to fabricate three-dimensional contents regardless of geometric complexity created a new typology of characteristic designs, components, tools and models.

These newly emerging of these generic fabrication properties were based on previous technological innovations in neighbouring disciplines that then developed into a new innovative manufacturing process.

The technological developments integrated include: -

Servo technology—vital for the control of the nozzle or laser movement of additive manufacturing technology—was developed in the 1940s and 1950s by MIT’s Servomechanisms Laboratory (MIT Library 2010), mainly for military applications.25 These findings were later embodied substantially in the numerical control mechanism of a post-war innovation called the “Motor controlled apparatus for positioning machine tool” developed in 1952 by Parsons and Stulen (1958) and picked up by the first generation of additive fabrication developers.

-

UV hardening of photosensitive polymers developed in 1945 (Agre 1945)

-

Development of the “Ruby Laser Systems” capable of generating and amplifying coherent light (Maiman 1961). The laser allows the emission of light with a narrow wavelength spectrum (“monochromatic” light) that could then be altered for the UV hardening process of stereolithography.

-

The combination of early mesh-based modelling techniques and tool path control derived from Automatically Programmed Tool Language (APT) by MIT’s Servomechanisms Laboratory Computer Application Group (Ross 1978) bridged the gap between design and motion control.

The genuine technological characteristics portrayed in chapter 1.1.5 remain persistent today, despite individual industrial improvements in the field. It can be expected that these tectonic and processural properties of additive manufacturing will also play a major role in guiding the technology’s evolution in the coming years and thereby allow those research strategies that focus on these aspects to provide sustainable content in the face of an altered technological environment.

Contemporary disciplinary and interdisciplinary innovations improve the capabilities of individual additive processes but can also affect the conditions of the technology as a whole. Recent attempts to implement additive fabrication in a chain of related manufacturing technologies that connect nano-material research (Brice and Herman 2005), bespoke print materials (Kumar and Kruth 2009), heterogeneous materials with electronic wiring (Malone, Berry and Lipson 2008) and hybrid models that integrate multiple components (Weiss et al. 1997) from different manufacturing chains26 can be seen in this context. The passage that the technology was taking, from representation towards an increasing interest in a distinct typology of fully functioning components, interweaves the fabrication method with other technologies like material science, structural mechanics and chemistry among others and relies upon an integration of such knowledge fields in addition to its own. Additive fabrication therefore must be regarded not as an individual technological stream, but rather as a “domain” within a larger territory of scientific development that

24

For a full report on the developments and applications over since 1996 see Wohlers (1996-2011)

25

The research institute engineered a servo-control system for advanced radar used on U.S. Navy ships. The lab’s war-time

developments were concentrated on fire control and gun-positioning instruments.

26

For detailed information see section 4.2.2 Integrated additive manufacturing.

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continuously alters its application and technological boundary conditions around the core characteristics portrayed above.

Keeping with the territorial analogy, we can imagine such technological progress as being characterised by constant modulation of its topography in a time-based sequence in which the historical developments reach a state of temporary stability but nevertheless continue to exert an impact on novel developments by cross-referencing and recontextualising information across multiple domains and over time.27 The general morphology of such “territory” is guided by the technology’s inherent core characteristics, outlined above, which are then shaped locally by the individual manufacturing applications. These individual technologies have distinct characteristics of process, scale and application, but can potentially alter the character of the overarching domain through processural innovations.

The described integration of additive fabrication into a process chain of other computer-aided manufacturing technologies can be understood in this context. This blending between different previously isolated technological domains can thus initialise a new and characteristic manufacturing chain. A methodological approach can develop a systematic model that integrates these described properties and potential transformations on a global and local scale and guide a research strategy for this thesis.

3.1.1 Domain and subdomain Following the preliminary nomenclature, the technological domains encompass a principal processural quality that is actualised in the subdomain through a specific assembly of manufacturing technology and functional application. The better terminology for comparable properties in natural science appears well suited for application here. In the field of material science a physical differentiation is made between intensive and extensive material properties that describe characteristics that are not bound up with scale, and others related to environment and measurable quantities.

“Extensive properties include not only such metric concepts as length; area and volume, but also quantities such as amount of energy or entropy. They are defined as properties which are intrinsically divisible: If we divide a volume of matter into two equal halves we end up with two volumes, each half the extent of the original one. Intensive properties, on the other hand, are properties such as temperature and pressure, which cannot be so divided.” (Delanda 2002, 25) Delanda further characterises the relationship between intensive and extensive properties “While an extensive map shows the product of a process, the intensive shows the process itself.” (Delanda 2005, 6).

The extensive property represents a real-world materialisation of an intensive potential within a metric and physical space. The “intensive” property, in contrast, defines material characteristics that are consistent regardless of scale or material quantity. Projecting these qualities onto the research methodology would correlate the inscribed manufacturing properties of additive fabrication to intensive, and individual technological applications of such to extensive properties representing distinct states in which the intensive properties are realized. These extensive characteristics compose the final artefact with its specified spatial, functional and technological boundaries by a goalbased selection of manufacturing method, fabrication materials and scales. These terms are better suited to describe the properties that we previously designated as domain and subdomain and will be used from here on.

This research strives for a perspective that can simultaneously inspect both the intensive and extensive impact of the experiments. Extensive research results can point to developments and challenges in the local technological environment and simultaneously question the quality of the intensive property from a broader stance. The extensive

27 Laminated Object Manufacturing (LOM), a paper-based additive manufacturing process, ceased to exist by 2000 and has been recently revived with novel fabrication properties (Mcor Technologies 2011), which adapted the technology to contemporary technological and financial requirements but also eliminated the obstacles of the historical process.

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specimens that will be produced in the experiments are hence constructed to facilitate such an interconnection between extensive materialisation and intensive property. In contrast to previous research on rapid manufacturing that was connected to a specified milieu and functionality—as seen in the examples of prostheses (Kai et al. 2000) and mechanical engineering (Vashishtha, Makade and Mehla 2011)—the experiments are guided by an abstracted and transferable demonstration of the intensive properties of additive fabrication. The findings gained from these extensive specimens will elaborate future alterations of the intensive and extensive manufacturing properties but also inform other fields. The aspects of material-based performativity researched here can thus provide an intensive design property that delivers a new architectural planning instrument which can actualise extensive materialisations within site- and scale-specific boundaries. Intensive properties thus contain a dynamic potential that can develop into innovative technological processes with new extensive and intensive properties for the distinct discipline or beyond.

3.1.2 Global and local transformation A methodological understanding of these interactions requires a dynamic model in which such complex behaviour can be integrated. In the course of the research an inspection of catastrophe theory appeared promising to help comprehend these dynamic developments, interactions and abrupt changes between different interacting conditions on many scales. The research extracted a general conception of the decisive properties of the kind of model guiding this research approach. The systematic understanding and terminology derived from this theory can be found in numerous places in the thesis and delimits the overarching conceptual space the investigation inhabits.

Catastrophe theory, first published by Rene Thom (Thom 1973) in his book Structural Stability and Morphogenesis, marked an influential contribution to the mathematical understanding and description of dynamic system behaviour.

It first delivered a model for the explanation of morphogenesis in all aspects of nature, while remaining general enough to allow it to be applied particularly effectively in those situations “where gradually changing forces or motivations lead to abrupt changes in behaviour.” (Zeemann 1976, 65). Soon after its introduction its applicability as a research method for studying and predicting systematic behaviour more broadly was investigated.

Thom favoured this aspect, as documented in the following article: “The catastrophe model is at the same time much less and much more than a scientific theory; one should consider it as language, a method, which permits classification and systematization of given data.” Thom cited in Woodcock and Davis (1978, 39).

Catastrophe theory saw applications in physics in research on elastic structures and thermodynamics (Poston and Stewart 1997), as well as animal behaviour, economics, politics, sociology (Isnard and Zeemann 1976) and psychology.

A fundamental perspective that catastrophe theory advances for the description of potential and equilibrium conditions within a dynamic system is illustrated by an experiment conducted by Woodcock and Davis in 1978.

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Ill. 6 A simple catastrophe: A sudden change in potential energy (illustration from Woodcock and Davis 1978, 48)

Woodcock describes his experiment as follows: “The vertical axis represents levels of potential—call it height […]. The x (horizontal) axis represents some condition—call it the straight-line distance covered on the roller coaster—whose value determines the value of the potential. Now imagine that you can place a ball at any point on the curve. At all but four points the ball will immediately begin to roll. Those four points, the four places where the curve has neither upward nor downward slope are equilibrium points. One is a “ledge”, one is a “hilltop” and two are the “bottom of valleys”; only the two minima are points of stable equilibrium; the point of inflection is semi-stable, and the local maximum is unstable” (Woodcock and Davis 1978, 45).

Woodcock’s illustration describes the conditions for a sudden change of the ball’s position under four points of varying stability. A dynamic behaviour that would alter the values on the x and y axis remains acceptable as long as no sudden shift from a stable equilibrium to a jump or a catastrophe occurs. This topological invariance that underlies a form-change constrained solely by preservation of its equilibrium is responsible for the evolving processes and possible abrupt changes under the given framework. The boundary conditions of Woodcock’s diagram identify a systematic model in which the given position of the ball would define a local state in varying equilibria conditions. Applied to understanding the field of additive fabrication, one can correlate the principal boundary conditions to the intensive properties that are shaped by manufacturing characteristics and related properties, like the choice of material. The extensive materialisations created through a combination of both would occupy a local state of equilibrium until a potential jump occurs—triggered by changes within the boundary conditions—that could then trigger an alteration of the principal conditions. All extensive materialisations that do not alter the intensive properties could be understood as different states of unique minima of the overall system.

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Figure 1-Material and application development of additive manufacturing

The above diagram (Figure 1) tries to visualise such behaviour for the shift from rapid prototyping to rapid manufacturing that was informed by changing technological conditions. The principal boundaries for this model are defined by (a) the additive manufacturing process properties and (b) the materials employed in a chronological sequence that identifies the technology’s application. Initial additive fabrications relied on materials with weak mechanical properties; accordingly, the technology was utilised for representative functions. Extensive individual materialisations created changing states of equilibrium expressed by variations in the applied technologies and research goals, but did not cause a general change of the overall application scheme as such. It was not until the arrival of metal sintering processes (MacCay 1995) that a sudden shift took place in the applicability and the scale of the created objects. Yet rapid manufacturing applications did not commence instantly after the material was introduced, but required a series of extensive investigations that remained in a state of equilibrium within the prototyping sector until it was finally conceptualised and applied for manufacturing purposes. The enhanced mechanical functionalities were blended with a concept of full-scale components with fully functional properties to elaborate the new application typology of rapid manufacturing for low-quantity production. The recent efforts undertaken by the ATSM commission (ASTM International 2010) to standardise the quality of additive fabrication materials and processes may prompt another jump in the technology’s applicability in the future. The implementation of additively fabricated elements that do not require component-specific quality measures but grant a quality norm to the process itself can facilitate a wider spread and more economical integration into industrial applications and workflows since it would eliminate the need for costly component testing.

Accordingly, one has to investigate how ongoing innovations in the manufacturing and computational design processes are feeding back into the intensive and extensive properties and what their potential for a characteristic change could be. The intensive properties that characterise additive fabrication have remained constant over long 62

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stretches, and it is expected that they will gain further importance in the future as a result of stronger integration into the manufacturing processes of characteristic components that exploit the technology’s potentials. The research conducted here therefore incorporates an analysis of both the extensive materialisation and the potential jumps in intensive properties. This approach should provide for findings that can be employed in research on the momentary state of technology, but also allow projections into broader and future fields of knowledge within additive fabrication and other disciplines.

This cross-linked perspective practiced in the conceptualisation and later analysis of the research projects is implemented methodologically in the thesis and can be seen in the active integration of interdisciplinary research in the literature review, experiment processes and later projection of the research findings, as in e.g.

-

Interdisciplinary implementation of auxetic and functionally graded material research

-

Correlation of historical developments in architectural design processes to contemporary research

-

Analysis and transfer of textile assembly systems to computational design processes

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3.2 Application in the thesis This perspective that focuses on the systematic interconnection between intensive and extensive properties in additive fabrication, but in other fields of knowledge as well, will appear specifically in three main parts of the thesis.

I.

Adaptivity of the experimental findings

The experiments are designed to demonstrate intensive properties of novel additively fabricated materials and digital design approaches that should allow them to be applied later to the extensive realisation of a concrete design task.

Although the experiments are conducted using an extensive set of tools and processes, the focus of their materialisation is so abstract that it should be possible to revisit, adapt or alter their underlying principles to distinct extensive conditions in the future. Although extensive in their materialisation, the experiments strive for intensive insights.

II.

Perspective on technological progress

The technological history of additive fabrication has shown that the intensive properties were not established per se, but were the fruit of recombining a number of related technologies. Additive fabrication and digital design were based on a series of prior developments that developed over time into a new manufacturing system.

Parsons and Stulen’s innovation of 1958 was initially developed to mechanically cut and bend planar sheet metals with computer-guided servo control and—through the coupling with other technologies—was able to be transformed to materialise three-dimensional content. Such an adaptation process “collapsed” the initial 2D process and “unfolded” a new manufacturing principle through a novel assembly of suitable technologies. The intensive quality inscribed in the subtractive cutting process was changed through the new thresholds emerging from the additional innovations of laser technology and polymerization, which would shift the organisation of the process into a new manufacturing system with new intensive properties.

Following this logic it appears plausible to assume that contemporary and future technological developments within additive fabrication research hold the natural potential to collapse again into yet another technology that further expands the scope of the manufacturing spectrum. This aspect will be considered in the analysis of the individual experiments and the conclusion of the thesis.

III.

Design process

Intensive and extensive properties play an important role in the understanding, analysis and synthesis of the investigated design process.28 The principal reactivity of the digital tectonics and the employed printing material are approached as intensive properties that reveal their extensive properties through the materialisation and resulting performance of the artefact produced.29

28 29

See section 4.3.2 Digital design and material performance.

For a more detailed description see section 4.3.3 Relationship between the design and process.

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3.3 Further research methods The research strives to “triangulate” the accumulated extensive and intensive information, by implementing findings from a variety of different research methods that will be addressed specifically in the later experimental chapters. The idea is that the “involvement of practically all our human senses, as well as other independent sensory instruments, is more likely to give us a comprehensive and ‘rich’ perspective on the research issue being explored” (Gray and Malins 2004, 32). This research will accordingly develop design specimens, 1:1 samples and include experimentation with materials and processes, modelling, and simulations, and use metaphors and analogy. The reflection and analysis process of the physical and digital experiments will employ different visualisation, photography and 3D models, finite element modelling methods and the variant approach by Bhashyam, Shin and Debashish (2000) for performancebased material distribution.

To investigate the performance of the test samples in the first experiment, an adapted testing apparatus is constructed based on the same principles as Rehme and Emmelmann’s device of 2009. Mechanical testing procedures are used to determine compressive properties (ISO 604:2002 Norm) in the second experiment. Magnetic resonance imaging (MRI) is employed for visual inspection.

This methodological approach expands on the earlier conception that “Rapid Prototyping can potentially support a comprehensive and integrated environment to study form, space making and the physics of materials relative to machine processes in construction” (Sass and Oxman 2005) by paving the way for a potentially fruitful integration of the experimental findings into a future intensive property in related disciplines beyond additive fabrication.

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Literature Review

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4.0 Organisation of the Literature Review The literature review will be organized in accordance with the research questions and thus divided into three sections. The critical overview portrays the state of research within the respective fields, but information disseminated in one of the fields may, of course, be relevant and complement neighbouring research topics and should be understood accordingly. The literature review follows a methodology that projects findings from the disciplines of material science, textile research, and architectural history among others. This approach is driven by a perspective on technological progress that operates by projecting, altering and implementing multiple input sources into novel fabrication systems or concepts.

The first two reviews inspect a distinct field from material research that deals with auxetic structures (I) and functionally graded materials (II) and their existing applications within additive fabrication research. Although auxetic materials have been around for only just over thirty years, there is already a vast body of applications and research on the topic. The review will focus on the individual structural principles that can release such behaviour in two and three dimensions and appear suited for potential translations to digital and additive fabrication workflows. Research on molecular auxetic design, for instance, is mentioned, but not dealt with in detail. Due to the novelty of the process, research literature in the field of additive fabrication of such structures is limited and therefore covers mainly texts from material science, especially on the parameterisation of structural solids and functionally graded materials.

The final review, corresponding to research question III, covers literature from art history, architectural theory and philosophy alike, lending this section a broader scope.

The literature review will also give explanations of the individual processes and definitions from material science that might not be familiar to the architectural reader and exceed the scope of a classical review.

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4.1 Literature Review Research Topic I The review presents key literature that allows the identification of suitable structural components and the relevant characteristic properties that could be computationally described and comply with the fabrication constraints. This overview will lead to identification of the selected building block from the field of auxetic foams. These materials show form-changing performance in two and three dimensions through a distinct structural composition that can be digitally parameterised and fabricated. Relevant historical and contemporary research on the conceptual and physical investigation of these materials in different scales will be assessed accordingly. This dimensional separation will also be reflected in the later experimental structure and should provide the reader with the option of cross-referencing between the experiment and the literature.

4.1.1 Identifying the structural component The research question centres on an investigation of additively fabricated materials with inherent form-changing capability that can be calibrated digitally through the composition of their microstructure. The first step in this research direction is to delineate suitable configurations that enable such a mechanical behaviour and which can be translated to computational and fabrication processes alike. The research concentrates on materials with cellular logic and behaviour that can be controlled by calibrating the configurations of the internal building blocks.30 Generative methods for optimised structures that could be employed for such a process will be presented in the literature for research topic II and not dealt with here in any detail.

An in-depth analysis of the mechanical behaviour and the internal structural composition of materials can be found in the key publications Cellular Solids by Gibson and Ashby (1988) and the follow-up Cellular Materials in Nature and Medicine (Gibson, Ashby and Harley 2010). The books provide insight into the properties of cellular materials through an analysis of natural materials and their translation into abstracted geometric representations that can be exploited for engineering processes. The texts explain the mechanical and geometrical properties of microstructures in many dimensions under different load-bearing scenarios and provide parameterisations of their constituent building blocks. The material described covers the behaviour of corks, foams, corals and cancellous bones, among others, and gives precise information on their dependent structural logic and abstracted geometric representations that allow the reader to correlate mechanical performance with structural composition. The later publication provides information on artificially created foam structures of titanium and tantalum (Gibson, Ashby and Harley 2010, 223-249) for biomedical applications, but offers no further documentation on additively fabricated processes that would allow rapid manufacturing of such structures. First translations of natural bone structures into a geometrically defined digital archive of space-filling shapes of controlled density have been achieved by Bucklen et al.

(2008). This research developed a series of cellular solids with defined interfaces between neighbouring cells that compose foam-like structures with functional geometries for application in tissue engineering, yet does not propose any future manufacturing process that could cope with the geometric resolution and the required scale.

As far as the later digital design and the modelling of such structures are concerned, the cellular pattern of foam structures appears especially interesting for several reasons: -Foams sub-divide a given volume into three-dimensional substructures whose exact nature, the target of geometric and material research for centuries, has been well documented.

Research on emerging structurally differentiated constructions is potentially very interesting in this context, but will not be investigated here. Biomimetic translations of these structures can be found here: Turner and Soar (2008), J. S. Turner (2005).

30

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Several cell geometries have been acclaimed to be optimal shapes for filling the space of a given volume with discrete cellular elements, whereby the tetrakaidecadhedra (Ill. 7), discovered by Lord Kelvin at the end of the 19th century (Kelvin 1887), proved to be the most efficient for a long time. Only the recently developed Weaire–Phelan structure is able to pack space more efficiently (Weaire 1997).

Ill. 7 Kelvin structure (Kelvin 1887) -

Foams can be structurally differentiated into open-cell and closed-cell foams. In the former the solid material is drawn into the struts that form cell edges. The individual foam cells contain no membranes to their neighboring cell. “These struts join at the vertices—usually, but not always four cell edges meet at each vertex—that is, the edge connectivity is four.” (Gibson and Ashby 1988, 15). Open-cell foams appear to be a valuable field of research for additive fabrication since the cellular openness allows for uncomplicated removal of the support structure.

-

Polymeric foam structures can show a periodic distribution of their identical space-filling cellular units or can have locally specified variations that depend on the chosen manufacturing techniques. Regardless of the cellular composition (as open or closed foams) and the underlying lattice configuration (as a periodic or non-periodic array), the foam’s distinctive structure can be portrayed in terms of topological principles. Even the most random natural and synthetic foams always obey these topological rules. Connectivity and structural order have been described by Deshpande, Ashby and Fleck (2001) and can provide an understanding of the predominant elements (Ill. 8) to be coded in a later digital design. Only a limited number of elements have to be taken into account to change a structural behaviour. The topology of individual cell composition appears essential for a material’s load-bearing performance under stress or strain.

Ill. 8 Mechanism (a) and structure (b) in Deshpande, Ashby and Fleck (2001)

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The pin-jointed element “a” would collapse under vertical load as the struts rotate around the joints. In the element “b”, a triangulated structure supports axial loads and creates tensile or compressive forces in different struts. A topological ruleset would define the difference between (a) and (b) by defining the connectivity of the horizontal ball joints. Structure “b” has three connectors that produce a horizontal sub-division of the four-sided polygon. This single difference in the structural ruleset is responsible for a significant change in the properties of the material.

The encoding of these connectivity parameters allows the creation of foam structures that have a performancedriven metrical materialisation of topologically invariant relationships. In this case the material is not composed by a periodic three-dimensional array of identical elements, but can be designed to show a performance-based differentiation of the geometric position of the element’s individual nodes in keeping with the defined topology. In research by Hanna and Mahdavi (2004, 8-12) the authors use stereolithography to create a polymeric foam structure with such heterogeneous structural properties and develop a digital workflow for the calibration of such, which will be described in a later chapter.

4.1.2 Auxetic materials A survey of the literature on structural solids pointed to an interesting type of foams that was discovered in the late 1980s by R. S. Lakes (1987), which bear structurally driven inherent form-changing potential that seems suitable for investigation in this thesis. These “auxetic materials” show counterintuitive properties under longitudinal stress and strain that create multilateral expansions or contractions. Andrew Alderson’s paper “A triumph of lateral thought” (Alderson 1999) on the structural mechanics, application scale and functional use provides a first comprehensive overview on the topic.

Mechanical behaviour of auxetic materials Conventional materials tend to contract perpendicular to the applied load under bilateral strain and expand under stress.

Auxetic materials behave in an opposite manner and expand under lateral strain. This mechanical property is described by a negative Poisson ratio. This intensive value expresses the ratio of contraction or extension in the perpendicular direction in response to an applied load and its degree of extension or compression in the direction of application (Ill. 9)

Ill. 9 –Left: Poisson ratio with positive value, right: Poisson ratio with negative value

The Poisson ratio can be deducted from these metrical conditions according to the following formula:

In the left diagram one can see that the thickness of the material in the lateral direction decreases under strain. The resulting ∆d is smaller than the initial value and has a negative prefix, yielding a positive Poisson ratio. In the right diagram we can see 70

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

that ∆d increases its thickness and has a positive prefix, resulting in a negative Poisson ratio. The material performance presented here can also be witnessed in the reversed sequence of forces. Conventional materials with a positive Poisson ratio will expand under such a force flow, whereas auxetic materials with a negative Poisson ratio will have a smaller lateral value that leads to compression of the material. The following list presents the Poisson ratios of a number of natural and synthetic materials.

Poisson ratio of various materials31 natural rubber ν= 0.50 stainless steel ν= 0.30 titanium ν= 0.14 cork ν= 032 gold ν= 0.45 diamond ν= 0.07 beryllium ν= 0.02 re-entrant foam ν= -0.7 (R. S. Lakes 1987) Auxetic materials are interesting because they show enhanced mechanical and physical properties that classify them as both structural and functional materials.

“The development of structural materials is focused on improving their mechanical or physical properties, often with a saving in weight or cost. By contrast, functional materials are designed to detect and/or respond to events or stimuli that occur during their lifetime. These materials often display novel and counterintuitive behaviour.” (Alderson 1999) It appears especially valuable to investigate such combined structures for future architectural application since they can be employed for a series of materials with integrated functionalities, three-dimensional form-changing potential and even increased impact resistance properties, an aspect that has been thoroughly investigated for lattice structures

by Obrecht, Reinicke and Walkowiak (2009) and proven mathematically for periodic cells by Dirrenberger et al.

(2011).

Upon vertical impact of an object with auxetic material properties, the neighbouring material expands in the lateral direction towards the impact zone. This surplus of material is given an enhanced protection layer of material between the object of impact, without increasing the overall thickness of the material. This property can lead to thinner structures with increased shockabsorption properties. Auxetic materials have raised interest in the defence industry for its potential as a material for novel body armour.

Successful creation of auxetic properties in three dimensions relies on structures with changing bulk densities. Bulk density can be calculated as the ratio between the mass of material and the volume that it occupies. In an auxetic process the occupied volume of the material expands while the mass remains invariant. This process requires that part of the mass be integrated into the volumetric envelope of the material before the activation process and has the option to expand under strain. According to Lakes and Wineman, this material property is not monotonous but can vary over time. This aspect presents an important insight for the digital calibration of graded auxetic cell structures that exhibit varying states of ligament unfolding and thus variable Poisson ratios, which differ not only locally, but also over time.

All values retrieved from Mott and Roland (2009) except where noted.

Cork has a Poisson ratio of 0 and remains invariant in its diameter under stress or strain. Wine bottles that are sealed with cork remain airtight, making for an easy sealing process since the material does not expand under a vertical load and provides for a stable seal.

71 31

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“…Several systems are known which exhibit a Poisson ratio that increases with time. For example, in the glass to rubber transition of polymers, the shear modulus may change by three orders of magnitude, but the bulk modulus changes by about a factor of two. In isotropic solids this corresponds to an increase in the Poisson ratio from about 0.3 to nearly 0.5 with time…” in Lakes and Wineman (2006).

This aspect will have an effect on the implementation of the experimental conditions addressing research question I and will be explained there.

Auxetic behaviour can be witnessed on all scales (Ill. 10) of simple and composite materials.

Ill. 10 Auxetic materials in different scales (Alderson 1999, 385)

The properties of the chosen geometric molecular or structural microstructure appear to be responsible for such behaviour. The digital parameterisation of this property would hence allow structures to be adapted to the available additive fabrication scale under the required structural conditions.

Auxetic properties can be found in natural materials, but most of the employed materials are of artificial origin.

Natural auxetic properties can be witnessed in the cow teat (Lees, Vincent and Hillerton 1991) and in cat skin (Veronda and Westmann 1970). A form of silica (SiO2), α-cristobalite, exhibits Poisson ratios of +0.08 to -0.5.

Natural arsenic materials can have such anisotropic material properties in various structural directions. These materials show positive and negative Poisson ratios ranging from +0.5 to less than -1 as described by R. Lakes (1993). Synthetically produced auxetic materials are seeing an increasing application in the aeronautical, automotive and medical sectors.

Alderson (1999, 390) lists the following selected inventions and patents: Biomedical applications -

a dilator for opening the cavity of an artery or similar vessel for use in heart surgery and related procedures (Moyers 1992)

-

auxetic surgical implants (E. A. Friis 1991)

Automotive/aeronautics -

A manufacturing route for auxetic composites (C. K. Toyota 1998) 72

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-

A drive unit for feed-gear rotation formed from auxetic material (J. K. Toyota 1997)

-

Auxetic fibre-reinforced composite skin with lower resistance to motion (Yamaha Corp. 1996)

-

4.1.3 Two-dimensional auxetic structures Common auxetic materials can be divided into extruded two-dimensional auxetic patterns and three-dimensional auxetic foam structures. The following text will present research developments of auxetic geometric patterns in two and three dimensions, their respective applications and identify candidates for experimental research.

Re-entrant bow-tie structure Several geometric methods on the cellular level exist for the generation of two-dimensional auxetic structures that determine the auxetic performance of the overall material.

The most common auxetic structure is composed of interconnected mirror-symmetric cells in a bow-tie or butterfly shape, as was first described by R. Lakes (1993). The specific geometry of this building block allows re-entrant activity of the individual ligaments under stress in the x and y-directions (Ill. 11). Under longitudinal strain the reentrant planar elements are driven towards the direction of the force and thus expand in the x and y-directions.

Ill. 11 Left: non-auxetic material performance under longitudinal stress, right: lateral expansion in an auxetic cell structure (Alderson 2005, 14)

This auxetic principle can be observed on many scales. Recent research conducted by Alderson et al. develops an idealised conception for the creation of molecular-level polymeric networks that are analogues to the geometry of macro-scale auxetic honeycombs (Alderson, Daviesy et al. 2005). This experiment investigates the theoretical design of molecular structures with pore sizes that can work as host systems for the release of nano-scale materials (e.g. for applications as drug molecules) in the form of buckyballs (Ill. 12). The mechanically activated release of such molecular components can be controlled solely by the stress or strain parameters of the host pore’s size and shape. “…The entrapment and release of guest molecules within the layered honeycomb structure is determined by variations in the pore size and shape. Pore size and shape variation with applied stress can be more easily achieved using a high volume change negative Poisson ratio structure than a lower volume change positive Poisson ratio structure.” (Alderson, Daviesy et al. 2005, 21)

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Ill. 12 Sub-unit of theoretical auxetic molecular network: “(1,4)-reflexyne”. (Alderson, Daviesy et al. 2005, 34)

Macro-scale auxetic materials with a bow-tie structure have been fabricated using -

Additive fabrication in different materials by Rehme and Emmelmann (2009) using stereolithography (SLA) for polymeric and selective laser melting (SLM) for metallic materials (Ill. 13)

-

Technical knitting conducted at the research group at University of Massachusetts in Dartmouth under Professor Ugbolue (Ugbolue et al. 2008). (Ill. 13)

Ill. 13 Left: SLM-fabricated sample of auxetic structure (Rehme and Emmelmann 2009), right: auxetic warp knit structure

by Ugbolue et al. (2008)

All of the above produced materials have yet to find larger-scale industrial application; they have been produced and studied for experimental purposes only. It has been concluded from the experiments on bow-tie cells—independent of the scale of the auxetic structure—that the Poisson ratio is determined predominantly by the enclosing angle= θ of the bow tie shape as shown in (Ill. 11), the scale of the cellular component overall, and the connectivity between the individual modules that relies on the mechanical properties of the employed material. Larger angles increase the re-entrant character of the cell and result in a lower Poisson ratio. According to Lakes the structure is “orthotropic,

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however by appropriate choice of the rib widths and angles, an elastically isotropic honeycomb with a Poisson ratio of -1 can be obtained.”

(R. Lakes 1991, 2290).

Consequently, a material with a gradual orthotropic material quality could be generated by controlling the rib’s width and angles.

Isotropic materials have identical mechanical and physical properties in all three dimensions. Orthotropic materials show different properties in their orthogonal directions. A classic example for such a material is wood, which has distinct mechanical properties related to its fibrous composition.

A future parametric model will have to encode these relationships if it is to control the Poisson ratio of such a bowtie structure successfully. All experiments that have been performed so far employed a periodic distribution of the cellular bow-tie geometry. Cells with gradual θ values have not been tested. Structures with varying cell geometry present an interesting research field for potential form-changing processes that can be integrated into a material’s structure and fabricated with additive manufacturing. The experiment will therefore investigate bow-tie auxetic cells with graded θ values that can be described well in a digital design model.

Curved surfaces Auxetic honeycomb materials show a three-dimensional deformation that can form shell-like shapes. Since the spatial deformation is directly related to the Poisson ratio of the cells, it can be conjectured that double-curved freeform geometries can be designed by defining internally the rib widths and angles responsible for determining the Poisson ratio. The potential uses of double-curved moulding and shaping panels for car body parts and aircraft components has been described already by Burke (1997). The so designed structure evolves through an applied strain force that initiates the spatial bending process and releases a pre-stressed freeform geometry that is frozen in position through the application of two outer layers of deformable composite material.

Since the complexity is embedded in the geometry of the individual cell’s morphology, not in the refined activation mechanism that exerts the pressure on the honeycomb structure, the construction that is responsible for the stress and strain forces can be built in a less complicated fashion. This fact points to the inherent advantages additive fabrication technologies have to offer, especially in connection with other fabrication technologies. Since the technology of production is indifferent to local alteration, fine detailing, geometric irregularities and material complexity can be integrated to achieve a rich scope of performances. The thus defined complexity can then operate successfully—as described above—with components of lesser complexity and tolerance. The following section will demonstrate this approach.

One-dimensional auxetic performance Bubert et al. developed an experiment for creating morphing wing profiles by altering the auxetic bow-tie module.

For this purpose a one-dimensional auxetic node with unilaterally retracted ligaments was developed, which allowed the form to change in one direction, keeping width constant as the material elongates. Such a continuous change in the form of surfaces may enable beneficial applications in high-performance environments. The design of an airplane wing is such a case and has been studied by McGowan et al. (1999), Thill et al. (2007), Maheshwaraa, Seepersad and Bourell (2007). The alteration of the wing profile in accordance with an environmental, aerodynamic or functional requirement was part of the earliest flight technology.

Improvements in the reactivity of the wing’s surface and its modulation resulted in enhanced flight performance, control and safety. The Wright Brothers’ first airplanes used a technique known as “warping” (Anderson 1985) that twisted the wing in 75

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the lateral direction for flight control. Contemporary control of the wing’s profile is based mostly on efficient roll control achieved through hydraulically driven telescopic profile changes. Several research groups33 are investigating wings that can change their shape with adaptable profiles that incorporate integrated auxetic structures. “Current research is primarily dedicated to various conformal changes, namely, twist, camber, span, and sweep. It has been shown that morphing adjustments in the plan form of a wing without hinged surfaces leads to improved roll performance, which can expand the flight envelope of an aircraft, and more specifically, morphing to increase the span of a wing results in an overall reduction in drag, allowing for an increased range of flight.� (Bubert et al. 2008) Bubert`s team investigated a composite wing structure consisting of an actuator substructure fabricated from simple hinged U-shaped aluminium profiles to drive the longitudinal elongation process, an additively fabricated auxetic one-dimensional core material with a Poisson ratio = 0, and a soft, thin silicone elastomer sheet with orthotropic carbon-fibre reinforcement called a flexible matrix composite (FMC), which served as the outer shell and environmental interface. An extension of the wing length by 100 % was tested. Through a one-dimensional auxetic structure with a Poisson ratio of 0 the wing would expand in length while the width of the material remained constant to provide enough in-plane stiffness to allow good aerodynamic performance. In order to achieve such an effect the researchers used an adapted bow-tie cellular pattern with a one-sided re-entrant geometry as shown in Ill. 14. Conducted tests proved that a lateral elongation by 100 % could be achieved while maintaining an acceptable stiffness value.34

Ill. 14 Left: standard, auxetic, and modified zero-Poisson cellular structures (Bubert et al. 2008, 5), right: morphing wing components: zero-Poisson RP substructure and actuator with air muscle

In this successful experiment it becomes obvious that the technological effort employed to achieve complex performativity is moderate. In contrast to comparable form-changing structures that use hydraulically linked mechanical performative layers and require high degrees of precision and intensive servo-based steering technology for each of its discrete members, a performativity inherent to the material, which comes from these novel cellular solids, implies simplification of the required components, steering technology, production costs and maintenance.

This result points to interesting architectural applications that will be further explored in an experimental investigation of graded one-dimensional auxetics. The design of structural components that show high strain values and significant form-changing potentials released in a tuned fashion could offer potential for dynamic building Among them are the Advanced Composite Centre for Innovation and Science (ACCIS) Department of Aerospace Engineering, University of Bristol, UK and the Aerospace Engineering Department of the University of Maryland.

34 For increased bending stiffness the structure later introduced carbon-fibre rods located under the elastomer sheet.

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performance that adapts the geometry of its components to external boundary conditions for performance. Since additive fabrication allows effortless local modulation of its geometrical content, structures with a gradual alteration in their bow-tie geometry can be studied. Several geometric conditions are responsible and can be configured geometrically using architectural modelling tools. Lower θ values amplify the bow-tie appearance and extend the length of the re-entrant ligament that later unfolds irregularly under strain force.

For the auxetic property to appear the cell must be able to unfold its internal ligament completely until θ values reach a value of zero. High numeric differences in the θ values of neighbouring cells in the x and y-directions can potentially result in internal blocking of cells with a high θ value. Cells with low θ values reach the state of complete unfolding earlier and then behave like materials with a positive Poisson value, resulting in a longitudinal extension that follows the direction of the strain. This shift from a negative towards a positive Poisson ratio can prevent cells with a high θ value located in the neighbourhood of these low θ value cells from exposing their auxetic character, since the ligament geometry cannot unfolded completely.

It is thus estimated that gradual distributions of the θ values will allow better control of the auxetic properties of the material over time as previously stated by Lakes and Wineman (2006). In the description of the experimental setup, the research will further examine these boundary conditions for the definition of bow-tie geometry and the threedimensional distribution of the cells.

Chiral honeycomb Another type of cellular component that unfolds auxetic material properties is called the “chiral honeycomb” and was developed by Prall and Lakes in 1996 based on R. Lakes’ studies of the mechanics of such structures (R. Lakes 1991). The auxetic performance can be created by “circular elements or nodes of equal radius r joined by straight ligaments or ribs of equal length L.” (Prall and Lakes 1996, 305). This group of vertically extruded linear ligament structures is tangentially attached to four circular elements (Ill. 15). When a lateral strain is applied to the structure, the ligaments are unrolled tangentially along the cylindrical elements. The drawing shows that the auxetic effect depends on the angular relationship between the individual end points of the ligaments and their length. In the diagram the end points are differentiated by 60 ̊ or 120 ̊ angles. The extruded cell (which yields a honeycomb structure) is two-dimensionally “chiral” and has hexagonal symmetry.

The chirality of an object can be defined by the absence of a rotational axis of deflection. The most prominent example illustrating such a chiral property can be seen in the hands. The left and right hands relate to each other like a picture and its mirrored image. No rotational action can create congruence between both hands.

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Ill. 15 Chiral auxetic cell (Prall and Lakes 1996, 8)

The lateral expansion is created by a circular unrolling that is initiated by the momentum of motion around the centre of the cylinder. The auxetic performance initiated in this manner works differently than the bow-tie system discussed above. The course of the ligament activated by the lateral strain resolves in a curved figure resembling a cycloid.

The cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line. For a precise definition of its geometric construction see Lockwood (1963, 81-89) Here the cylinders are equally responsible for the lateral and longitudinal expansion of the material. In the above mentioned bow-tie method the ligaments have a structural role centred on an either longitudinal or lateral expansion of the material. Axial normal forces along the centre lines of the ligaments are in operation whereas the chiral honeycomb structure is activated mainly by various lines of momentum applying force to the end points of the ligaments and the cylinders. Several research institutions, like the Department of Aerospace Engineering of the University of Bristol, the Department of Mechanical Engineering of the University of Sheffield and the Negative Materials Group of the University of Malta, are investigating an application of these auxetic structures for components with controlled formchange.

A series of these experiments investigate composites with an auxetic core and various shell materials (Ill. 16).

Common sandwich panels rely on a fixed internal topology of the honeycomb material. The EU-funded FP7 research project CHISMACOMP has developed a novel fabrication method on flat and curved sandwich panels with increased electromagnetic (Meli et al. 2009) and structural performance for bended beams with an internal chiral honeycomb structure (Cicala et al. 2011).

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Ill. 16 CHISAMCOMP panel developed by the University of Catani, Italy (Meli et al. 2009)

The control over the panel’s auxetic properties allows the curvature of the sandwich to be adjusted by applying a folding process that provides a novel method for the creation of shells with synclastic35 curvature and enhanced structural behaviour as stated below.

“Standard cores and honeycombs act mostly as spacers between structural laminates (skins). Honeycombs and cores are usually difficult to bend. Auxetic materials overcome these limitations. Due to their peculiar deformation mode (i.e. they expand when stretched rather than contracting) auxetics can bend without any saddle effect typical of honeycomb structure.” (Cicala et al. 2011, 2) The promises and challenges for additive fabrication lie in developing these versatile materials with novel mechanical properties so that in the future they can replace a reductionist assembly system with a more holistic utilisation of material. The layered assembly of isotropic materials could then be replaced by an immediate production process that would generate performative structural composites with complex performances and simple fittings. Another interesting aspect can be seen in the three-dimensional spatial deformation potential of such structures, since they can provide a novel method for creating curved shell structures. These structures would be a combination of tensile constructions with persistent strain forces to activate the auxetic behaviour and load-bearing shells that are potent in handling stress forces along the surface.

Auxetic behaviour from rotating squares In the year 2000 Grima and Evans presented an innovative structure (Ill. 17) that showed bilateral auxetic performance under stress/strain forces. The authors describe the mechanism as follows: “…In this letter we present a new mechanism to achieve a negative Poisson ratio. This is based on an arrangement involving rigid squares connected together at their vertices by hinges as illustrated (Ill. 17). This may be viewed as a two dimensional arrangement of squares or as

Synclastic properties can be found on surfaces with continuous positive Gaussian curvature. When the curvature is negative at all locations a surface is called anticlastic.

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a projection of a particular plane of a three-dimensional structure. This latter type of geometry is commonly found in inorganic crystalline materials.�

Ill. 17 Auxetic behaviour of rotating squares (Grima and Evans 2000, 1563) In this case the evolving Poisson ratio is not constant, but depends on the applied strain force that controls the rotation of the individual squares.

Similar structures can be found in Îą-cristobalite, which exhibits Poisson ratios of +0.08 to -0.5. These materials have been referred to as molecular auxetics by Alderson (1999, 2). Other molecular auxetics can be also found in cubic metals and liquid crystalline polymers.

Variations to the rotating squares structure described above can contain unilateral triangles (Grima and Kenneth 2006), parallelograms (Attard, Manicaro and Grima 2009) and rhombi (Grima, Farrugia et al. 2008) as recent investigations have shown.

4.1.4 Three-dimensional auxetic foam structures The auxetic materials described in the previous paragraphs are constructed from two-dimensional patterns that are extruded in their z-axis to form a honeycomb. These structures have positive Poisson ratio in the z-axis and exhibit auxetic behaviour only in the x and y-directions of the surface. Such materials can be valuable for panel-like building elements, which are interesting for their longitudinal and lateral form-changing capabilities. The rotational bending of such planar structures for cylindrical elements has been investigated by Jackman et al. (1998) and would allow lateral expansion under strain force along a cylindrical envelope. The design of structures that can have a tri-axially auxetic performance requires differently structured cellular component geometries. Research in the field of material mechanics was slow to discover the structural elements responsible for the creation of auxetic materials shaped in this way, so to date only few have been parameterised.

In 1987 R. S. Lakes produced the first three-dimensionally auxetic foam structure with isotropic auxetic properties (Ill. 18).

For manufacturing, conventional low-density open-cell polymeric foam was used that was compressed in all three directions and placed in a mould. The foam was then heated up slightly above the softening temperature and later cooled down to room temperature. The material was then removed from the mould and tested.

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Ill. 18 Right: Conventional open-cell polymer foam, left: re-entrant foam with a Poisson ratio of -0.6 (R. S. Lakes 1987, 1039)

In the mechanical test the thus manufactured new material showed a compression-dependent Poisson ratio. Higher multi-lateral compression leads to a lower Poisson ratio. The initial foam was structured by open space-filling tetrakaidecahedra, as the tri-axial compression exerted on the edges of these cellular elements protruded them inward and resulted in a re-entrant geometry. Foam structures based on dodecahedron elements have been used by Evans, Nkansah and Hutchinson (1994) to develop a finite element approach for modelling the structural properties of auxetic foams.

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Re-entrant knots Lakes presented two idealized cellular geometries (R. S. Lakes 1987), (Friis, Lakes and Park 1988) that show this reentrant geometry so applicable for the digital design of structural building blocks. Both cellular geometries share similarities with the two-dimensional auxetic bow-tie structures in respect to the way the linear ligaments are folded to create the auxetic effect.

Ill. 19 Left: idealised re-entrant unit cell (R. S. Lakes 1987, 1039), right: idealised re-entrant knot structure (Friis, Lakes and Park 1988, 7)

The two presented knots appear suitable for an experimental investigation since the spatial performance of the hinged pipes is well understood geometrically and can be embedded in a cellular array with simple connectivity parameters.

Keyed brick structures A different type of auxetic cells with high-bulk properties has found application in historical reactor cores on a macroscopic level. Alderson describes the achieved functionality and performance as follows: “These cores were developed in the late 1950s and so pre-date the bulk of auxetic materials research by some 30 years. Indeed, these structures were not designed specifically to have auxetic properties. Instead, they were made to withstand the horizontal shear forces generated during earthquakes, while also allowing free movement of the structure in response to thermal movements between the graphite core and steel supporting structures, and expansion and shrinkage of the graphite during exposure to radiation. A Magnox reactor core is made up of free-standing columns of graphite bricks, with central channels for the fuel and control rods. The bricks connect the loose sides and corner keys in keyways. The structure expands in all radial directions when subjected to a tensile load and, furthermore, retains its square lattice geometry during deformation.� (Alderson 1999, 384385) Alderson sketches a diagrammatic description of the spatial elements that composed these cores. No further information could be retrieved on the exact fabrication method for such structures, which were engineered back in the 1950s. This aspect would be rewarding since the diagram depicts a three-dimensionally arrayed cubical assortment with integrated moveable connector elements that must have posed challenges to macro-scale fabrication procedures at the time they were developed.

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Ill. 20 Magnox reactor with three-dimensional auxetic structural composition (Alderson 1999, 385)

An investigation into a graded distribution of these cellular elements with high-bulk density requires a more complex digital modelling process that respects the dimensional relations between cubical elements and the brick keys. In a gradual distribution designed to affect the relational measurements between these elements, analysis would have to address complex structural frictions that occur, especially under non-orthogonal stress or strain. These aspects excluded this cellular solid from further experimental investigation in this thesis.

Hexagonal lattice cells with curved bi-material ribs A recent study by Lakes (2007) presented an additional parameterized auxetic foam module with bended ligaments composed of dissimilar materials. The calculation defined two abstracted material properties complementing the ligament’s geometry that would lead to varying elongations within the element under temperature change and thereby allow calibration of the materials’ extension. This thermal property would constitute a bending momentum within the ligament that allows control over the form-changing properties of the material.

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Ill. 21 Hexagonal lattice cells with curved bi-material ribs (R. Lakes 2007)

This aspect could present an additional research field, since multiple materials can already be printed today with Objet’s Connex technology. Yet it is questionable that a temperature-dependent form change in the material properties would exert a recognisable effect on the structures due to their similar molecular composition created by a blending process of two similar polymeric source materials. Furthermore these distinct volumetric entities would increase the amount of geometric information required for the printing process and thus exacerbate a constraint that is already critical today for simpler cellular structures.

4.1.5 Critical summary The research question addresses the investigation of a new type of additively fabricated materials with dynamic properties driven by structural differentiation. Open-cell foams have been identified as an interesting research subject since they provide a strict geometric framework on the modular and structural levels that allows computational translation and positive fabrication prospects. The dynamic spatial properties that have been discovered in auxetic foams promote experimental investigation for their form-changing potentials to elongate a component along all axes under lateral stress. This counter-intuitive behaviour in one, two and three dimensions is achieved through a spatial array of the cellular components compiled as open-cell foams. Existing production methods for auxetic materials do not take the local configurations of the individual cells into account, but rely on a process that fabricates the clustered cell geometry uniformly. Precise control over the internal deformation behaviour that occurs within the material itself cannot yet be steered with a sufficient accuracy. The deformation behaviour of such materials thereby depends (J. Grima 010, 59) on: -

shape of the rigid unit

-

degree of aperture

-

connectivity

-

rigidity of the unit

The characteristic properties of computational design and additive fabrication would allow these properties to be calibrated and hereby contribute to the existing research. The presented components that show variations in their cellular behaviour in all dimensions can be translated as a set of hinged linear elements that follow an encoded

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kinematic36 behaviour operating on the Cartesian coordinates of the individual end points of the lines. The digital model would thus be implemented to: -

Control the hinges’ degree of freedom

-

Control the range of the overall displacement reactivity through calibration of the cellular sizes

-

Control the individual nodes’ displacement reactivity through a definition of the permitted range of movement that would mark a transgression from negative to positive Poisson ratios.

The position of each node can be described by a set of coordinates. These coordinates, responsible for the degree of re-entrance, can be easily varied in relationship to an associated performance profile that corresponds with an expected Poisson ratio. Positive Poisson ratios can be therefore described through a re-entrance value of 0 that represents the lower boundary of the numeric range. In the modelling process the cells that have an encoded translational value of 0 would therefore show no re-entrant activity. For values >0 a successive displacement of the distinct node occurs in the re-entrant direction of the cell.

The given range of potential translational activity can be defined by the designer and drive the general reactivity of the structure in regard to a future Poisson ratio through parametric control of the θ values and/or the cell size of the element. This sensitive control mechanism can even create three-dimensionally anisotropic auxetic performance. The control over the numeric ranges of the individual movement axes of the nodes yields control of the range of possible re-entrant behaviour—and a modelled Poisson ratio. The sensitivity to which the auxetic material performance can be calibrated with such a method far exceeds the possibilities of conventional compression-based processes used for open polymer foams. The experiments will therefore investigate one-, two- and three-dimensional foam structures with a gradual distribution of their auxetic values and conduct mechanical tests to assess their performance.

“Kinematics is the branch of mechanics that treats the phenomenon of motion without regard to the cause of locomotion. In kinematics there is no reference to mass or form: the concern is only with relative position and change.” in Bottema and Roth (1979).

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4.2 Literature Review Research Topic II “There exists an increasing need for extending conventional CAD/CAM systems beyond geometry to consider material attributes (e.g., material composition and microstructure) inside heterogeneous objects.” (Bickel et al. 2010, 1)

The research question focuses on an investigation of materials with heterogeneous composition driven by threedimensionally graded distributions of mechanical properties. The chapter introduces the contemporary and historical research on graded materials with heterogeneous functional profiles and presents manufacturing options of such materials. This schematic description of the manufacturing processes and their respective tectonics is used for potential application transferred to the field of additive fabrication. The review will be thematically ordered to provide I.

Transferable knowledge from functionally graded material research for employable tectonics of thus created materials

II. III.

Insight into contemporary multi-material additive fabrication research Goal-based design processes to correlate structural performance with the allocation of a material

The review draws parallels to biological and botanical structures that employ structural hierarchies for functional purposes. These natural materials often contain multiple layers of structurally and mechanically differentiated hierarchies that allow a performance-driven morphology to emerge. The interconnection between different layers of functional entities from the molecular scale upwards drives a material- and performance-oriented tectonics that is surprising and efficient. The literature review will present examples of these functionalities and point to emerging possibilities presented by integrated additive fabrication processes for a future production of such materials that rely on multi-material assemblies from different technological sources.

Additive fabrication processes with multiple materials—introduced to the market only recently—promote the investigation of material heterogeneity in a single build process. Through the inherent characteristics of additive manufacturing even three-dimensional gradients of heterogeneous materials can now be envisioned that contribute to the existing scope of two-dimensionally graded materials.

The review will not cover voxel-based processes as investigated by Gershenfeld (2005), Lipson and Hiller (2010), Hiller and Lipson (2009), Popescu and Gershenfeld (2006), which, although interesting in their novel system of material assembly, still need further development and have seen only small-scale application to date. Such studies look at a novel distribution system of the employed materials that is not based on jetted droplets of different lighthardened materials that require exact positioning systems, but composes mechanically differentiated but geometrically periodic source materials that are assembled like LEGO blocks. This tectonics has consequences for the achievable tolerance of objects fabricated in this way, which would be defined solely by the self-alignment of materials, as shown for spherical geometries by Hiller and Lipson (2009), Lipson and Hiller (2007) and for other geometries by Hiller and Lipson (2009), and could also pave the way for recyclable fabrication materials as proposed

by Hiller and Lipson (2009). This assembly method will eventually implement research on programmed matter in the form of complex-shaped self-aligning chips as shown in Tolley et al. (2008) or contain silicon circuits in plastic (Stauth and Babak 2006) among others. This research field bears great potential for multi-material additive 86

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fabrication of complex materials, but actual physical artefacts are rare and small-scale and will therefore not be dealt with at this juncture.

The review presents contemporary research on the additive manufacturing of two- and three-dimensionally graded materials. Although on a small scale, these examples can help to argue for a different, entirely digitally created form of materials that have a graded distribution of mechanical and functional profiles and can help to project principles for future architectural applications.

A goal-based material design approach has to be developed to deliver an approximation of desired deformation behaviour through the meso-scalar assembly of materials. The review will present contemporary research in these fields and outline characteristic workflows on how the distribution of the material has been be controlled digitally and tested. Contemporary research on the implementation of these processes for a novel design understanding of computationally controlled materials will be presented in the literature review related to research question III.

4.2.1 Structural hierarchy and heterogenisation The prospect of additively creating materials with bespoke internal composition and material selection bears the promise of making a useful contribution to contemporary fabrication methods in terms of structural efficiency, reduced material consumption and the enhanced functionality of thus created elements. A reference to biological organisation supports this assumption and serves as starting point for the research.

Material and structural diversity can be traced on many scales in natural materials that are geared to fulfil a manifold of distinct functions simultaneously. The materials usually “exhibit weak macro-scale mechanical properties […], and yet, they are able to achieve orders-of–magnitude increases in strength and toughness.” (N. Oxman 2010, 55).

-

A dolphin’s skin, which is composed of an outer layer of porous material over a layer consisting of 80 % water and a secondary denser cellular material with integrated channels, can damp wave elongation during the swimming process and create potent propulsion effects through the interaction between the two layers (Hertel 1963, 190-199).

-

In a study by Amada, Fukao and Yuntao (2000) on the heterogeneous composition of layered bamboo materials the authors present a cascade of interlocked composite elements with functionally graded properties in the radial dimension of the bamboo (Ill. 22). The geometrical definition of the individual scale-dependent tectonic layers of molecular, fibrous and vascular cells are complemented with locally graded material selections that define and expand the overall mechanical functionality of the material as a whole.

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Ill. 22 Hierarchically graded structure of bamboo (Amada, Fukao and Yuntao 2000, 058)

The evolving fracture toughness that one can witness in specific risk areas of bamboo, which can achieve heights of up to 38.0 m, is higher than in other comparable wood materials due to the specific geometric articulation of the material layers and sub-layers. Bamboo is a multi-layered composite that follows regulated assembly rules for compliance with a desired performance profile, here flexibility and fracture toughness.

-

Load-bearing members employed in the human apparatus of locomotion have a graded materiality and show performance-based material and structural composition. The structural differentiation of compact human bone (Ill. 23) in contrast to cancellous bone (Gibson and Ashby 1988, 316-331) shows a hierarchical composite of geometrically and material-specific elements, molecules, fibres and embedded canals.

Ill. 23 Fibrous, laminar particulate and porous structures in compact human bone (R. Lakes 1993, 514)

These discrete elements are composed to comply with an expected performance profile that allows the bone to generate maximum stiffness values with minimum material investment and provide logistic pathways for the transport of nutrition, blood and oxygen. Dynamic and logistic functions can be integrated smoothly into this outer shell of the human bone and maintained over the organism’s lifetime.

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4.2.2 Integrated additive manufacturing Additive fabrication processes operate with a single material to create geometrically complex objects that have to fulfil mostly single purposes and hence cannot compete with the properties of natural materials. Materials can be geometrically calibrated to allow mechanical differentiation, but implementing performance through a cascade of structurally and materially differentiated layers is usually beyond the possibilities of additive fabrication. Yet a perspective that integrates additive fabrication processes in a sequence of other fabrication processes is beginning to develop in industrial and academic research, and perhaps will lead to industrially produced simple hierarchical assemblies. A sequential construction process that inherits and integrates complex components from other industries could point to a new characteristic typology of multi-functional objects with steerable mechanical, dynamical, electrical and structural behaviour that will eventually become a realistic new production option. Individual, discrete developments in the participating technologies can be then implemented and amplify the complexity of the later object that is constructed in such a fashion.

The combination of multiple manufacturing streams points to an interesting expansion of an industrial workflow that can be activated on many scales and in which Rapid Manufacturing plays an important role. Conducted research has focused mainly on applications in the fields of biomedical and robotic manufacturing.

Integrated fabrication processes -

Nanomaterial elements can be integrated into polymers used in additive fabrication processes for enhanced performative functionality. Koo et al. (2005) show that these materials, when blended with an even distribution of nano-composites, produce improved material properties with regard to flammability, and to thermal and mechanical behaviour. Kumar and Kruth (2009) provide a compendium of the current research on enhanced additive fabrication material for the creation of such composites with altered mechanical or functional properties and their respective fabrication methods.

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An example of multi-scale composite workflow can also be found in Lockheed Martin’s experimental research for the P-175 Polecat unmanned aerial vehicle (UAV) that uses a combination of additive fabrication processes with carbon nanotubes to materialise 98% of the airframe with a wingspan of about 27.0 m (Bloss 2007, 13).

Carbon nanotubes are discrete cylindrical elements with potent material properties exceeding the structural properties of steel and carbon fibre. They exhibit extraordinary strength and unique electrical properties, and are efficient thermal conductors. (Reich, Thomsen and Maultzs 2004) Beads of the fused material are stacked up under robotic control to fabricate a freeform part. Lockheed remains confidential about the exact manufacturing methods but currently holds several patents (Brice and Herman 2005) that describe additive-based methods of composite tooling effectiveness for improved part-to-part bonding. The patent described in the below figure (Ill. 24) might be a good guess.

In the patent diagram a powdered matrix and powder carbon nanotube material are combined in an additive fabrication process using a fusing beam from a laser or other heat source. This new additive fabrication technology uses a build material whose enhanced functionality is derived from a second technological process with related scales and enhanced functionality.

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Ill. 24 Rapid manufacturing of carbon nanotube composite structures (Brice and Herman 2005)

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The Shape Deposition Modelling Process (Weiss et al. 1997) integrates multiple manufacturing systems. Hereby mechanisms and multifunctional components are fabricated and assembled simultaneously. This combined technology allows the creation of bionic designs “that mimic the way biological structures are composed, with embedded actuators and sensors and spatially-varied materials.” (Cham et al. 2002).

Ill. 25 Shape-deposition modelling of “Sprawlita”, a dynamically-stable running hexapod (Cham et al. 2002, 2)

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Fibres, electrical wiring and fabrics that derive from alternative manufacturing technologies are compiled in a layered additive fabrication process. This technology allows the in-situ creation of fully functional objects like joints, hinges and cooling tubes for electrical wiring. Technological advancements in these embedded technologies can then be implemented in an increasingly complex object with a broad bandwidth of integrated functions (Ill. 25).

This combined interweaving of different areas of innovative manufacturing technologies is still in its infancy, but can nevertheless serve to demonstrate a future perspective on gradually cross-bred manufacturing technologies for creating and planning (Hatanaka and Cutkosky 2003) material composites with alternating mechanical and electrical properties.

In contrast to the presented bamboo example, which has neatly separated composite units (similar to an onion skin), a parametric modelling tool can provide for gradual changes between the different structural layers to enable a subtle translation between different functional zones. The division into primary, secondary and tertiary structural elements could then be traded in for a gradual accentuation of different immanent structural potentials. Such performance and structural stability is achieved with a minimum of material and a maximum of stiffness. Yet the goal-based design of such staggered structures poses great challenges to contemporary mesh-based analysis systems due to the potentially high calculation effort and complex interaction among the hierarchical structures.

This basic research on the implementation of composite manufacturing technologies into a single additively fabricated artefact can deliver interesting and innovative types of architectural elements that are not characterised by the sequential installation of their functional layers according to a construction timeline but rather merge multiple functions into a single fabrication process. The architectural consequences this process entails are potentially farreaching, since they affect the construction assembly, a classical formgiving parameter in building practice.

4.2.3 Functionally Graded Materials (FGM) For the conceptualization of 3D heterogeneous materials with specific mechanical behaviour and optimized topology (Hiller and Lipson 2009) one can draw upon a rich field of existing research conducted on 2D functionally graded materials. Hereby a linear alteration of the internal material distribution was investigated for creating functional components with differentiated performance realised by the controlled distribution of two materials in a laser-based fabrication processes. An investigation of these processes can potentially inspire design methods or representations for three-dimensionally heterogeneous materials and deliver functional applications for polymer-based additive fabrication procedures.

Research on the fabrication and potential applications of functionally graded materials began in the mid-1980s to help protect orbital rocket combustion chambers (Ill. 26) from de-lamination regardless of their thermal expansion, and to allow for a multiple use of the combustion units. Due to the extreme thermal differences within the components during orbital flights, mechanical failure due to different thermal extension ratios was probable. A graded distribution of the various heat zones—cold on the space-oriented sides with temperatures around 4K/-269 ºC, and warm on the parts oriented towards the propulsion and combustion engine—could be achieved only if the material distribution was reflected in the thermal transfer. This new material group for a gradual 2D-transition between pairs of materials was then coined Functionally Graded Materials (FGM).

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Ill. 26 Gradient coating of copper and nickel alloys in a rocket combustion chamber (Holmes and Mc Kechnie 2001)

The first major official national project developed in Japan was entitled “Research on the Generic Technology of FGM Development for Thermal Stress Relaxation� in the years 1987-1991 (Ichikawa 2001) and developed a variety of processes with different materials (like metals and their alloys (McKechnie and Richardson 1995), and ceramics (Watanabea, Yamanaka and Fukui 1998 )). FGM saw applications in developing tools for oil-drilling equipment (Agrawal and Roy 2003), hereby allowing the combination of high-wear resistance with high toughness expressed in a graded distribution of different metallic alloys (Ikegaya et al. 2000). Other research allowed the configuration of materials with free regulation of their electric fields. Functionally graded materials (FGM) with linear gradients are applied for corrosion resistance (Ichikawa 2001, 2), tunable optical electric properties, deterioration control and the electrical engineering of materials. This ability makes FGM materials applicable to many fields and allows the integration of incompatible functions within a single mechanical tool for the following applications (Myamoto et al.

1999, 4).

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rocket engine components

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engine components

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reaction vessels

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nuclear reactor components

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first wall of a fusion reactor

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lenses

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implants

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artificial skin

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building materials

Fabrication principles Since its initial innovation several fabrication methods have been developed that allowed a controlled 2D distribution of two or more materials. Since the existing research conducted in this relatively new discipline of material science is 92

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already vast and goes beyond the scope of this thesis, it has been decided to give a more systematic overview of the manufacturing technologies and assess their potential for transfer to an additive fabrication process. Myamoto et al. sub-divide the manufacturing principles as described in Ill. 27.

Ill. 27 Manufacturing principles of functionally graded materials (Myamoto et al. 1999, 163)

Classical manufacturing methods for functionally graded materials can be sub-divided into bulk, layer, pre-form and melt processes. Methods to achieve this objective can include “different mass transport mechanisms, or a combination of these that as well as solid, liquid or gaseous states.” (Myamoto et al. 1999, 163) -Bulk processes utilise bulk materials like powders, fibres or sheets and consolidate these stacked materials through pore elimination or infiltration.

A typical fabrication example for such structures can be seen in slip-casting, a technique used for ceramic casting. Hereby a cavity in a cast is filled with slurry particles of ceramic material. The capillary forces of the mould absorb the slurry liquid. The remaining particles—usually larger than the capillary channels—remain on the outer surface of the mould’s cavity. When the desired wall thickness has been achieved, the body is removed from the mould and is freed of excess material. Repeated slipcasting with different slurries can be used for the two-dimensional lamination of functionally gradient materials.

-Layer processing can be achieved through the mechanical deposition of material and employs lamination or thermal spraying techniques like plasma sintering (McKechnie and Richardson 1995).

-Pre-form processes modify existing gradients in a preform.37 “The conventional processes [for the fabrication of such structures] are solid-state, liquid or vapour-phase distribution. Graded fields can be used to introduce a gradient into the FGM.” (Myamoto et al. 1999, 164) -Melt processing operates with heated fluids that show complex fluid behaviour (rheological fluids). In this process a phase separation of the liquid, of polymeric or metallic origin, under normal or enhanced gravity delivers a structural “sedimentation” (Myamoto et al. 1999, 164) that can be tuned in its projected mechanical performance. Techniques like the Verneuil process (Shiota and Miyamoto 1996) for growing crystals delivers such gradients in the solidification process.

A pre-form is a tube-shaped container containing a thermoplastic material that is inserted through an injection moulding process.

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An abstracted perspective on the tectonic aspects necessary for the production of such graded materials appears interesting for potential digital translation. One can identify the sequenced distribution of material whose mechanical properties are altered either by its material properties (e.g. bulk processes) or through a change in the milieu in which the process takes place (e.g. melt processes) by gravity, centrifugal forces, etc.

The production environment of additive fabrication operates under constant temperature and uncontrollable aggregate states of the print materials and allows only a geometry-dependent distribution sequence of material diversity. The lessons to be learnt can hence be found in the geometric distribution system of FGM processes that can then allow successful implementation of such technological principles.

What are those principles from the creation of FGMs that can be inherited for an additive fabrication process? Of all the above techniques, material diversity is usually created through a sequenced distribution of material that is driven through an alteration of the thermal environment, gravity or material qualities. The manufacturing process that appears the most promising to assess is called “layer processing”. In this method a pair of powders in their plasma conditions is used for “spheroidization,38 melting, or the densification of plasma coatings or freestanding bodies.”

(Suryanarayanan 1993, 4). One additive fabrication process, laser-engineered net shaping (LENS), has already achieved this transfer between materials through local melting of differently distributed metallic particles. ”This solid freeform fabrication process […] involves laser processing fine powders into fully dense three-dimensional shapes directly from a computer-aided design model” (Liu and DuPont 2003, 1337).

Liu and DuPont employ this manufacturing technology to create a functionally graded material that combined CP Ti and Ti C powder. The two materials with a spherical micro-geometry were kept in two separate powder feeders. An in-situ mixing device, controlled by the rotational speed of the powder feeders, was used to transport the grained material into the respective nozzles, which were then exposed to an Optomec LENS system with a laser beam that melted the powder in a time-based sequenced to create the desired artefact. The resulting powder distribution can be seen in Ill. 28.

“Spheroidization is a widely accepted application of induction plasma technology. It basically consists of in-flight heating and melting of feed material followed by its subsequent cooling and solidification under controlled conditions (Tekna Plasma Systems 2009).

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Ill. 28 Graded distribution of materials with the LENS process (Liu and DuPont 2003)

In the microscopic images one can identify a gradual translation of scattered, nearly spherical, melted Ti powder (b) blended with a more homogenous Ti C material at the other range of the FGM spectrum (g). An analysis of this process reveals interesting aspects for transfer to a polymer-based additive fabrication process that will be explained below.

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4.2.4 Additive fabrication with two source materials The first part of the review has drawn parallels to existing processes from mechanical engineering and material science for the creation of two-dimensionally graded materials that now have to be teamed with contemporary research for additive fabrication processes with two or more materials. In the last step of this review these processes will have to be coupled with research on goalbased digital design procedures that merge material assignment and structural performance. The following paragraphs will inspect the current state of multi-material additive fabrication technologies.

Additive fabrication with air pockets as secondary material With the invention of air-filled soles by Marion Frank Rudy (Rudy 1977) the mechanical control of material performance through air pockets became an everyday experience. Ruby’s initial innovation was an insole with pressurised gas pockets that exhibited a low diffusion rate and maintained its performance over a long time span.

The shape of the integrated channels was constructed in accordance with the expected dynamic load to maximize comfort.

Ill. 29 Insole construction with air-pockets (Rudy 1977, 1)

Several researchers (Bickel et al. 2010), (Maheshwaraa, Seepersad and Bourell 2007) have transferred this approach to additive fabrication to control the bulk density of an elastic material or provide dynamic performance properties.

A method for structural differentiation of manufactured material is the calibration of the bulk density of a material. Smaller bulk values (expressed as g/cmÂł) express a higher percentage of porous material as opposed to a fully dense granulate. The structural relevance of such a change in material properties can be illustrated well with the example of cell structures and especially polymeric foams.

Air can therefore be considered as the second material employed for the creation of graded mechanical material properties. A change in the bulk density of a flexible material through different volumetric air pockets can then be used to define local elasticity values. This appears to be a rewarding field for future research since it only requires a consideration of the support material removal processes and would provide access to more mature materials like those used in stereolithographic (SLA) processes. SLA or Polyjet printing processes operate with a support structure material for overhanging geometries, which have to be removed mechanically and hereby constrain the choice of the scale and shape of geometric elements that can be designed. Closed cellular shapes cannot be accessed by the cleaning device and have to be configured as tubular geometries in an appropriate scale and build direction that 96

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allows for full removal of the support material. Once this removal process has been simplified the creation of even irregular tubular structures could be achieved.

Such a geometric approach is sketched in the following.

A lattice structure containing tubular elements is generated through a calibration of varying radii. The resulting individual cells contain a set of circles that can be parametrically driven by two- or three-dimensional numerical matrices to control the course and diameter of the evolving tubes (Ill. 30).

Ill. 30 Calibration of cellular tube geometry These changing tubular elements can be tailored in such a manner that varying degrees of bulk density could occur and hereby allow the control of locally varied elasticity of the material through its changing zones with pneumatically controlled tubes.39 A first test has been performed for the modelling of such structures. In this test an irregular distribution (Ill. 30) of numerical

Further differentiation of material properties can be achieved by filling of the air tubes with a liquid material. The liquid’s viscosity in combination with the positive matrix material given by the additive fabrication technology defines the range of elasticity. Future research can also implement findings on self-healing properties through tubular resin reservoirs that could be embedded into the solid freeform material. For a recent study on these self-healing materials and the application of tubular embedded structures see Trask, Williams and Bond (2007).

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values that was inherited by a 2D matrix common in contemporary finite element solvers was used and translated into differing zones of tubular geometry.

Ill. 31 CAD model of tubular structure and Zcorp plaster print

Darker areas would thus create thinner tubes and lighter areas result in wider diameters. A material test was printed with a Zcorp machine that proves this geometric calibration in a plaster material as shown in Ill. 31.

Support structure removal affects the scale of such tubular structures especially in the hard-to-reach areas inside of the panel’s geometry. The fabrication of isotropic hole structures with encapsulated air pockets within the void spaces—as in closed foams—are and will remain a continuing challenge for additive fabrication technologies.

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Bickel et al. 2010 apply a similar method to create a material sample with tuneable elasticity values by integrating a stacked array of tubes in a material sample. Here the authors apply a goal-based process in which layers of extruded honeycomb structures with differing tube radii are created, which are correlated with envisioned deformation profiles analysed from standard materials (Ill. 32).

Ill. 32 Additively fabricated base materials under 15N force (Bickel et al. 2010)

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To avoid removal processes and potential remnants of support structure material remaining inside the sample, the authors orient the periodic longitudinal tubes in the direction of the z-axis (Bickel et al. 2010, 5). To do this Bickel manufactured a sample with the Polyjet printing process consisting of an extruded honeycomb structure with two uniform tube diameters, and two outer layers as a base and a load distribution surface for mechanical testing. The thesis will later return to the author’s goal-based design process for the calibration of the geometric content.

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Successful tests with additively fabricated pneumatic structures have already been conducted on deployable wing profiles fabricated using an SLA-based printing technology by Maheshwaraa, Seepersad and Bourell (2007). This approach allows the calibration of a suitable wing following a digitally optimised deflection profile and the manufacturing of such for experimental purposes (Ill. 33). The authors present a method for the impregnation of the SLA part and demonstrate an air-tight sealing method to close the opening for the removal of the support structure.

Ill. 33 Deployable wing (Maheshwaraa, Seepersad and Bourell 2007, 10,11)

The Appendix of the thesis presents an investigation by the author and Bernhard Sommer on additively fabricated inflatable knot structures with stress-dependent limiters integrated in the flexible skin. This test reveals the existing constraints that are still imposed on the fabrication of such structures with regard to material brittleness and geometric complexity. The results of these tests are documented in Palz and Sommer (2009)

Additive fabrication with active implementation of support structure material Several AM technologies (such as FDM, SLA and Polyjet printing) operate with a set of two materials. In this pair the one material represents the actual model-building material, whereas the second provides the structural support for overhanging geometries and is usually eliminated after the curing process, by washing or mechanical removal procedures. These feed materials can contain a blend of two materials. In some processes it may be possible to vary the ratio of this blend to produce functionally graded composites as stated by Gibson, Rosen and Stucker (2010, 424) and Kumar and Kruth (2009).

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FDM tests have been conducted (Ill. 34) that used the secondary nozzle, normally reserved for the support material distribution, as an additional material that allowed the differentiation between various parts of the model by colour.

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Ill. 34- A skull model made of two materials (Gibson, Rosen and Stucker 2010, 425)

The skull with a black infill visualizes such a test sample, yet questions remain. Since the skull is a typical example of classical overhang geometry, a large amount of support structure would be necessary to stabilise the white-coloured print material during the manufacturing process. Yet it appears as if the black support structure is only present in the smaller areas above the right eye, which would not give enough structural support for the printing process to be successful. One can rather estimate that the two parts were printed in separate printing processes and assembled afterward.

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Recent research by Milos et al. (2010, 7) on the additive fabrication of sub-surface scattered materials has already actively implemented and manufactured such a support structure material for functional tests, but will be reviewed later. “We use the support material as the third material in our experiments, simply by leaving holes in the meshes that are then automatically filled.” (Milos et al. 2010, 7)

One can deduct that for a useful application of such bi-material processes the boundary conditions for support structure material have to be correlated to a specific geometry that can combine the two aspects required at specific times during the printing process: I. II.

Structural support functions of the first material during the manufacturing process to provide the foundation for material disposition Geometry with a different mechanical property that expands the functionality of the later artefact with FGM-like performance.

Multiple materials for biomedical applications Successful additive fabrication with two printed materials for the calibration of graded properties has also been performed in the field of medical application and bio-implants (Mookerjee et al. 2009) where a simultaneous layered distribution of “2% alginate hydrogel and a Dextran-infused calcium chloride post-crosslinker” (Mookerjee et al. 2009, 1) was achieved. The two employed components were fabricated with the help of an FAB@Home additive fabrication system (fab@home 2010) equipped with mechanically driven syringes that contain a natural alginate hydrogel and a matching cross-linker. These tests were successfully executed through an innovative material-dependent configuration of the material disposition system. A method was invented that would deliver precise control over the distribution of the two materials. In a reciprocating motion (Mookerjee et al. 2009, 4) two interconnected syringes would release or stop material deposition based on the activity of the neighbouring syringe. The employed print substance for the experiments was a mould-making material fabricated from brown seaweeds and an additional synthetic crosslinker.

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Crosslinkers can be defined as “A reagent that will react with functional groups on two or more molecules to form a covalent linkage between the molecules.” (Thermo Fisher Scientific Inc. 2009) Mookerjee et al. proved that, through a simple layering process, locally adjusted algae concentrations can be achieved that “can be used for medical applications such as multi-compliant, biocompatible implants and surgical planning. This technique can represent objects with differing stiffnesses which can give a more accurate depiction of the body parts within the patient.

Additionally, multi-compliant gel would also assist in producing implants due to its biocompatibility and cell encapsulation.” (Mookerjee et al. 2009, 9)

Ill. 35 Hydrogel print with multiple stiffnesses (Mookerjee et al. 2009, 7)

Printing electronic devices Toys with embedded circuitry and “electrical wiring, flexible circuit boards, strain-gages, electromagnets, electroactive polymer actuators, organic-polymer transistors, and electromechanical relays” (Lipson and Malone 2008), (Malone and Lipson 2008) have been produced recently.

The materials used, which are teamed with the structural polymer materials, consist of “polymers filled with a granular conductive phase. These include commercially available silver inks, our own ink formulations, and silverfilled silicone rubber. These materials have the benefit of simple, room-temperature processing, and are typically flexible, or even elastic, but the drawback of having relatively high resistivity—typically ~ 10-3 Ω-cm.” (Lipson and Malone 2008, 4). Yet further improvements in this area have to be focused on ease of production, surface finishes, and enhancement of the functional complexity and degree of electric efficiency of the created objects.

The presented tests, although innovative and surprising, point to the critical boundary conditions that multi-material additive fabrication still faces with regard to detail, ease of use and scale. The integration of air-filled pockets nevertheless shows an interesting future research field for dynamic structures that can take advantage of larger-scale processes if the geometry complies with the support structure removal procedures. This can be achieved through the build direction and the geometry and scale of the integrated vascular networks. Future research that utilises graded material voids for static constructions could also extend the historical research on graded composites with additively fabricated tuned armatures conducted by Gervasi and Crockett (1998).

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4.2.5 Additive fabrication with multiple materials Industrial additive fabrication with multiple materials has been a technological option since the introduction of Objet’s Connex technology in winter 2007. Several research activities have emerged that employ the technology for material tests beyond representational applications and investigate the technology for rapid manufacturing purposes.

The text will review research by Neri Oxman and present experimental approaches conducted on material distribution based on light scattering to mimic organic materials with additive fabrication (Milos et al. 2010).

Interpolating performance with material assignment In 2009 Neri Oxman used Connex printing technology to design a chaise lounge named “the Beast” (Ill. 36). The seating areas, which were composed of a cellular Voronoi pattern, used an intelligent material distribution of five printing materials to accommodate varying seating profiles, integrate load-carrying functions and materialise a structurally functioning whole. The images presented portray a 1:3 scaled-down prototype that corresponds to the available build size of the Connex machine. Oxman writes about the different performances realised in the design: “Beast combines structural and human-corporeal performance by adapting its thickness, pattern density, stiffness, flexibility and translucency to load, curvature, and skin-pressured areas respectively. Multiple algorithms were generated that correspond to these variables such that stability is mediated with pleasure, and structural integrity—with visual and sensual experience. … It is designed as a threedimensional object that provides for multiple seating positions, each promoting a completely different experience. The cellular pattern applied to its entirety is designed to increase the ratio of surface area to volume in occupied areas where the body potentially rests. A pressure map study was conducted that matches the softness and hardness of the cells to cushion and support sensitive and high-pressured areas. By analyzing anatomical structures that cause concentrated pressures, Beast becomes softer and flexible where pressure needs to be relieved. The relative volume of each cellular cushion is locally informed by pressure data averaged with values representing structural support and flexibility. Its density is informed by global and local mean curvature values such that denser, smaller cells are organized in areas of steeper curvature whereas larger cells are found in areas of shallow curvature.” (N. Oxman 2010, 220)

Ill. 36 Left: Voronoi pattern with Connex in-fills (N. Oxman 2010, 81), right: 1:3 prototype (N. Oxman 2010, 79-80)

The author describes a workflow that includes generated pressure maps which are translated into Voronoi tiling, and algorithmic distributions of the load- and curvature-dependent material selection. The printed model represents a first materialisation that has in mind a conceptual material approach to create a new type of designed objects, with varying properties that correspond to the localities of functions and calibrate a form and material selection around it.

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The chair inspires interesting application of such materials as an interface for the interaction between human perception or/and locomotion and materials. The chair is distinctly designed with a personal locality in mind that appears on the horizon as an increasingly feasible manufacturing option. It hereby re-centres the individual person through holistic communication between materials, structure and senses within a product of potential mass fabrication (N. Oxman 2010, 204).

Fabricating spatially varying sub-surface scattering The research conducted by Milos et al. (2010)40 employs the Connex printing technology for a fully functional test sample with scattered materials that mimic natural, mostly organic materials. The scattering of materials is based on the light-reflection parameters of materials. “…This suggests layering materials to print not only opaque objects, in which light immediately reflects from the surface, but also translucent ones, in which light penetrates into the volume and re-emerges at different points. The distribution of this scattering is crucial to believable appearance of materials such as human skin, wax, and marble.”

(Milos et al. 2010, 1) Sub-surface scattering effects can be achieved by examining real-world materials like marble, natural stone and jade.

Through an analysis (Ill. 37) of the light transport behaviour achieved by a projection of RGB laser beams, the individual scattering profiles from each colour laser analysis can be extracted from a point on top of a surface. These specific material conditions then can be correlated with the measured material properties for the respective Connex materials.

Ill. 37 Top: measurement of Connex material scattering profile, bottom: measurement of reflection profile of an arbitrary material (Milos et al. 2010, 2)

After the measurement has taken place, an optimisation is started that co-ordinates the samples’ reflection parameters with those from the available set of AM print materials. This set is translated into a meshing process that assigns the optimisation results to a layered geometry that allows additive fabrication of the object to be created.

Through this optimisation process light-scattering behaviour can be achieved, expressed by material differentiation, that allows a realistic reproduction of heterogeneous sample materials with an additive manufacturing technique (Ill. 38).

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For further research on sub-surface scattering, see also Dong et al. (2010 ).

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Ill. 38 Additively fabricated marble with sub-surface scattering optimisation (Milos et al. 2010, 10)

Since the described research process is based on an analysis of physical source materials that can be translated into physical reproductions with heterogeneous material distributions, future research could calibrate such heterogeneity not only to imitate, but to enable an innovative design of an entirely digitally calibrated set of materials with their own specific surface scattering profile. Since optimisation routines have already been developed, the future design of such a bespoke translucency can be envisioned and fabricated. In this sense the fabrication of materials that integrate functional requirements, translucency, privacy and openness is possible, materialised in a gradual distribution of three-dimensional material heterogeneity.

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Summary The research that has been already conducted in the field of functionally graded materials can provide useful methodologies for the description and configuration of material distribution that can be assessed for a transfer to three-dimensionally graded materials. The different composition systems borrowed from other disciplines like metallurgy41 are investigated for their transferability for use in additive fabrication. The experiment chapter will come back to this issue in the description of the modelling process and identify related tectonic systems that have been studied from 2D functionally graded materials.

Several methods are available today to create gradient materials with additive fabrication, yet contemporary research in this area seeking an application to produce fully functional components is scarce. It is estimated that this will change as more robust additive manufacturing materials become available, a greater variety of multi-material printing systems that integrate voxel-based approaches are developed, and the process for support-structure removal is refined. From the tests described one can envision architectural consequences that would influence the relationship between the individual and the material in different aspects of perception, use and interaction. The materials created are not only more closely related to the individual necessities of the human physiognomy and locomotion, but also establish a new formal tectonics with increasing biomimetic functionalities.

Additive fabrication also sees growing application, in the field of medical implant creation especially, mostly for the creation of biodegradable periodic scaffolding structures that allow controlled tissue growth. Very recent research by Pompea et al. (2003) and Hollister (2005) investigates composite structures with additively fabricated components that operate with FGM properties. These processes can be rewarding for a later investigation of bio-mimetic approaches, and interpretations of these technologies might be helpful in their projection for a future architectural practice that can implement materials with structural hierarchy.

4.2.6 Performance-oriented material distribution The following text will review research on digital processes for the creation of graded mechanical performance through calibration of an artefact’s multi-material sub-components. These techniques can bridge the existing fabrication technologies with a novel goal-oriented design approach that would allow the composition of tailored material compositions. Research in this area is still in its infancy as regards formal complexity and material differentiation and will see probable advancements in regard to speed, material diversity and calibration of fully graded materials. In 2000 Bhashyam, Shin and Debashish proposed a first integrated CAD system that would allow interactive and intuitive calibration of material heterogeneity and the three-dimensional visualisation of such.

This review introduces three design methodologies that are specifically geared towards the additive fabrication of heterogeneous materials and a process that has been used for the calibration of functionally graded materials in two dimensions. The approaches are structured according to a methodological separation by Bhashyam, Shin and

An historical definition of metallurgy initially described the science as followed: “Metallurgy, at the present understood, is the art of extracting metals from their ores and adapting them to the various purposes of manufacture.” (Percy 1861, 1-2) A contemporary reading of the term focuses on the impact of the materials’ microstructures for the definition of its mechanical performance and the respective manufacturing processes that alter these properties. For a good overview on the definition and the principles of metallic microstructures, see: Abbaschian, Abbaschian and Reed-Hill (1994, 2009).

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Debashish (2000) (Ill. 39) that is still valid today. They differentiate between “generative approaches” (Hanna and Mahdavi 2005), (Hiller and Lipson 2009) and “variant approaches” (Shin and Lee 2006), (Bickel et al. 2010).

Ill. 39 Left: variant approach, right: generative approach (Bhashyam, Shin and Debashish 2000, 122, 121)

Generative approaches In a generative approach the functional and structural boundary conditions are set by the designer and undergo an iterative evolutionary calculation process that negotiates material distribution, structural composition, density distribution or other properties. Once the calculation results have been received, a reverse engineering process is started that fits the graded material distribution into geometrically enclosed and mechanically specified volumes that approximate the generative results. Based on optimisation calculations, this systematic process “limits the role of the designer in the process. Further, tools for optimal design are limited and expensive and not easily achievable.”

(Bhashyam, Shin and Debashish 2000, 121).

In the research by Hanna and Mahdavi (2005) a topologically invariant cellular structure is spatially arrayed and transformed in such a manner that a goal-based load bearing scenario can be employed to calibrate the thickness of the branch-like structural members combined with the configuration of their spatial position. The authors present a technique “by which the internal material properties of an object can be optimised at a microstructural level (5x10-5m) to counteract the forces that are applied to it.” (Hanna and Mahdavi 2004)

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Ill. 40 Graded space-grid structure (Hanna and Mahdavi 2005, 78)

Hanna et al. create a structural fitness scenario that is then employed as the driver for the three-dimensional configuration of the cellular elements. This initial load-bearing scenario consists of a finite element model (FEM) of a one-sided restrained beam and a vertical force positioned on the opposing side of the structural element. In these FEM models an initial geometry is sub-divided into smaller discrete geometric entities of pyramidal or cubical shape that are defined by a pre-set number of nodal coordinates. The stress/strain effects on the nodes are calculated under load and resulting analysis data collected. In a next step a genetic algorithm is defined to counteract the applied forces by adapting the tubular diameters and nodal topology (Hanna and Mahdavi 2005, 80).42 “…The GA [Genetic Algorithm] randomly generates a population of topologies, and exposes each to the n-force conditions that were extracted from the cantilever beam. The sum of the average displacements of the nodes of each topology for all n-force conditions then forms the fitness of the topology, the objective being to find structures that deform less under the set load. By repeating this process for each topology, the whole population can be evaluated.

After many generations, the GA evolves a topology that can best counteract the range of force conditions.” (Hanna and Mahdavi 2005, 5) In so doing, FE analysis is used as a design driver that identifies the fitness boundary conditions for the composition and structural properties of the envisioned material. The position of such applications is reversed towards a design tool that is deployed not to validate a proposed design scenario, but to actively drive a morphological solution within abstracted boundary conditions.

Topology optimisation procedures for three-dimensional multi-material structures have been examined by Hiller and Lipson (2009), Gupta, Seepersad and Tan (2006) and for two-dimensional FGM processes by Silva and Paulino (2004). Hiller and Lipson’s method of optimisation is especially relevant for additive fabrication technologies for several reasons: The research method expands a well-established optimisation process by integrating multiple material properties that are aligned directly with the mechanical properties of Connex print materials (Hiller and Lipson 2009, 4). The research presented here is the first fully documented approach with the specific additive fabrication properties integrated.

The authors further integrated anisotropic mechanical properties in relation to the build axis in their fitness scenario (Hanna and Mahdavi 2004, 9).

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Topology optimisation is a finite element (FE) based process, in which material is redistributed within a virtual volume. In the material distribution process, or optimisation, the material is densified within the trajectories of the strongest working forces.

Bendsoe explains: “In the design of a topology of a structure we are interested in the determination of the optimal placement of a given isotropic material in space, i.e. which should determine which points of space should be material points and which points should be void (no material).” (Bendsoe 1995, 5) The material outside these trajectories is subtracted, leaving behind a structure in which the greatest structural stiffness is obtained with the minimum mass of material. The prerequisite for such a process is the definition of a design-space—the volumetric boundaries of the optimisation problem—and the simulated constraints and structural forces acting on this volume.

Through an iterative process that evaluates the structural requirements on the FE nodes, the material densifies towards a theoretical optimum, in which the deformation energy of the system is minimised. Such processes allow the creation of loadbearing members that comply with maximum stiffness ratios, while employing a minimum of material to resolve the structural boundary conditions. The process allows for adaptivity to design scale, resolution and material diversity that can be correlated with novel materials, processural speed and fabrication scale.

In the process the authors combine the classical homogenisation method by Bendsoe (1995) with a genetic algorithm that operates on spatially arrayed voxels with up to three assigned stiffness and Poisson ratios and their respective degrees of freedom. The voxel distribution is conducted in accordance with the investigated design space, here a beam. Analogous to finite modelling, discretisation operates these voxels as analytical entities that undergo evolutionary calculative steps until an optimisation of structural material distribution in the available materials is achieved.

Homogenisation is described by Hiller and Lipson (2009, 2) as follows: “This iterative process varies the effective stiffness of each cell within a 2D or 3D matrix according to its strain energy, and optimizes the structure subject to constraints on total volume and minimizing strain energy.”

The research used a deflected beam shape as its inspection model (Ill. 41). The genetic algorithm would then employ a representation that efficiently defines the sensible elements (genotype), in this case the material-specific voxel distribution, and uses a minimum number of elements. The material properties are transferred through an abstracted frequency model that develops a population matrix and releases a material distribution (phenotype) according to the applied loads. In contrast to the classical topology optimization approach, in which minimum density leads to the load-bearing structure, the approach conducted here follows a different approach: “We do not set a minimum density threshold, such that every voxel within the workspace is instantiated with one [of the three] materials.”

(Hiller and Lipson 2009, 3). In the shown illustration the genetic algorithm has conducted 15,000 iterations to achieve the described material-distribution process.

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Ill. 41 Left: employed Connex material properties, right: material distribution under vertical load (Hiller and Lipson 2009, 4,6)

Variant approach In the variant approach “the designer’s creativity, physical intuition and experience can be creatively exploited” (Bhashyam, Shin and Debashish 2000, 121). The process is not based on an automated system that operates without his intervention and requires interpretation, but facilitates the design, material composition, analysis and evaluation of the functionality and success of created objects through several design and analysis cycles (Bhashyam, Shin and Debashish 2000, 121). Unfortunately, the process is not developed far enough to realise these functions within a single software package and requires further usability improvements before a more straightforward approach can be achieved. Shin and Lee’s research on two- and three-dimensional problems explain this process.

The design process begins with the definition of heterogeneous material distribution within extruded tubular elements with varying functional requirements on the inside and outside surface areas. Lateral sections of the tubular element are then discretised by triangular sub-division meshes. The material properties for the gradual translation are selected from a material library and a distribution coefficient is defined. After discretisation an iterative algorithmic process is applied that correlates material distribution with the desired performative profiles between outer and inner areas of the tube.

Ill. 42 Sequence of the design process (from left): Coefficient of material distribution, graphical display of graded material distribution, resolving post-processed mesh geometry (Shin and Lee 2006, 665-666)

The quality of the analytical result is based on the sub-division resolution of the cubical or tetrahedral elements that define the points for analysis. As the resolution of the discretisation is potentially infinite, an optimisation of such structures must be conducted in manufacturing-scale resolution. Local mesh densifications for critical zones within the inspected part can provide for locally increased accuracy where needed. The sequential distribution is achieved by geometric traction through a series of Boolean operations that mimic the calculated distribution sequence.

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Bickel et al. apply this method for the additive fabrication of structurally differentiated composites with desired mechanical performance retrieved from preliminary FE analysis.

“Our main contribution is a goal-based material design approach that approximates desired mesoscale deformation behaviour by microscale materials through combinatorial optimization.… Our algorithm receives as input a description of the object surface, examples of desired force displacement pairs, and a set of base materials with known deformation properties expressed in our non-linear material model.” (Bickel et al. 2010, 4).

Then the research follows a two-step process that helps to simulate the deformation of materials with tubular substructures.

I. II.

A primary Connex material with measured mechanical properties is used as a gauge material.

The secondary material with included air tubes is printed and tested under properties identical to those of sample I. In the following step the material properties achieved are aligned with the initial fully dense material so that in the future these properties can be transferred to structurally differentiated materials in a facile process.

Ill. 43 Correlation of fully dense material properties with structurally differentiated properties in simulation and physical tests (Bickel et al. 2010, 6)

This sub-division into a primary composite followed by a differentiation into heterogeneous materials allows a faster calculation of the effects of thicker or thinner base materials (Bickel et al. 2010, 2) due to a limitation of non-linear behaviour that can be usually witnessed in complex material composites.

4.2.7 Critical summary The processes presented here prove that material properties can be digitally modelled and analysed, and physical specimens fabricated additively and tested. The generative and variant procedures presented affect the designer’s involvement in the workflow and his control over the final product. Hiller and Lipson’s generative method is interesting for its freeform distribution of material, but poses challenges for integration into architectural workflows 110

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due to the complexity of the mechanical and algorithmic processes at stake. The geometric resolution of larger structures creates further obstacles for robust design evaluations due to the calculation efforts needed to compute these genetic algorithms. One can hope that these processes will follow a path similar to classical topology optimisation procedures, which are undergoing seamless integration into computational modelling software (Altair 2011) even today and put a novel formal vocabulary with inscribed structural properties at the designer’s disposal.

The variant approach, on the other hand, provides a more straightforward method to calibrate the design properties of heterogeneous materials and allows wider formal freedom for the initial shapes that can be tested. Future work will have to be geared around establishing material and structural archives that would allow the direct implementation of existing test results from others to a distinct design problem. Archived properties would naturally have to include the differentiated properties of the available materials in regard to build direction. Web-based archives in other disciplines exist, like the Cambridge Crystallographic Data Centre (Allen 2002), which provides exact structural and analysis information for three-dimensional molecular geometries and could inspire the development of such a knowledge base. Industrial multi-material additive fabrication technology will probably develop systems soon that allow the in-situ mixing of print materials that could directly transfer digitally retrieved material distributions as geometric post-processing through Boolean operations and other methods become obsolete.

This will take advantage of the novel *.amf file format for additive manufacturing (ATSM 2011), which can represent the specific mixing values and contains more data-efficient geometry descriptions than existing *. stl file standards..

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4.3 Literature Review Research Topic III

“It is only because architecture is haunted by shadows and ghosts, who drift from room to room murmuring old stories into the ears of their occupants, that its successive traditions project the appearance of a disciplinary unity� (Picon, Petit and Allais 2004).

Research questions I+II investigate a technological workflow for the design and additive fabrication of graded material properties, through either alternation of internal microstructural composition or bespoke calibration of discrete material properties. Research question III addresses these developments from a larger architectural perspective that goes beyond the more technological aspects to look at the preconception, analysis, representation and character of architectural design that can emerge from such a novel design practice. In this thesis the latter will not be examined in a purely theoretical approach, but an applied experimental study developed as experiment III, which illuminates these aspects. The literature review on this topic thus will develop the framing theoretical boundary conditions and references through which this experiment should be read and understood.

The literature review mirrors contemporary developments in computational design, fabrication and material engagement in the design process with analogies from the Renaissance, when a comparable evolution of architectural geometry and direct fabrication occurred. The introduction of a novel geometric protocol in the Renaissance altered the relationship between the designer and the designed and introduced variability, flexibility and novel formgiving parameters to a design workflow that evolved into derived typologies and tectonics. This view appears rewarding since interesting parallels can be detected, analysed and fed back into our contemporary discussion. Such a discussion can furthermore augment our contemporary perception of digital design by integrating it into a territory of architectural knowledge that generates historical and conceptual connections, disruptions and continuities. This aspect of conceptual interconnectivity follows the general methodological outline of the thesis that spans across this distinct perspective on the research process.

4.3.1 From the drawn to the built Additive fabrication introduces an altered relationship between manufacturing and geometry that allows the fabrication of geometric complexity and local variation without a simultaneous rise in manufacturing time. The factors that determine the scale of achievable detail are defined solely by the additive manufacturing process and the coherence with the required digital volume representation that can be post-processed to deliver sectional instructions to the print head or laser beam. This independence between geometry and manufacturing time represents one of the key innovative properties of the technology.

In historical hand-made processes, geometric complexity and detail often represented the mastery of a craft. Traditional Chinese wood carvings characteristically consisted of realistic three-dimensional hand-made materialisation of, e.g. scenic landscapes sculpted with great detail made out of a single piece of wood or jade (Jian and Quihui 2006). The achievable complexity was 112

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the fruit of a lifelong artistic learning process in direct interaction with the material, usually conducted without a detailed drawing and implementation of traded knowledge from the craft.

Given the fact that additive fabrication makes the materialisation of geometric complexity effortless, the focus has shifted increasingly in the direction of refined computational geometric procedures as the locus of the designer’s activity to define the subject of such materialisation procedures. The underlying computational procedures that compose such objects have expanded the classical—pre-computational—scope of architectural geometry protocols, like descriptive and Euclidian geometry, which nevertheless still serve as the ruling framework of design practice for the majority of architects. However, history can point to architectural works that already implemented alternative mathematical procedures into seminal buildings like Corbusier and Xenakis’ Philips pavilion for the Expo ‘58 (Burry and Burry 2010, 12).

Computational tools have obviously proliferated in the last years in their scope of usability and functionalities, complemented by numerically controlled fabrication processes, thus extending their impact into the domain of direct manufacturing. The initial separation between the designer and the fabricator persistent through centuries has been altered through an engagement of the digitally skilled architect with access to fabrication technology. Digitally derived direct manufacturing information in file-to-factory processes have therefore been the main topic in the practice and scientific community of digital architecture in recent years (Schoch 2005, Hovestadt 2010, Kolarevic and Klinger 2008). Computational design methods were developed for production cycles of well-established digitally driven manufacturing tools that feed their parameters back into the design process. Computational development within architecture has left its traces on the scope and character of the design practice and has been discussed thoroughly in the architectural community by Ceccato (2001), DeLanda (2002) M. Burry (2003), Reiser (2006), Lynn (1999), Holzer (2009) and others.

Brian Massumi describes the impact of these technologies responsible for “generating a “post-heroic” architecture. Massumi calls it “Postheroic, because these architects are focusing on processes and techniques rather than the end form.” (Spurr 2008, 49) In the past, geometrical innovations in architecture would often commence as mere representational tools, graduating to design (Hübsch 1838) and occasionally on to manufacturing. In the seminal research by Robin Evans (R. Evans 2000) on the relationship between architecture and its geometries these streams were delicately outlined for the pre-digital era. Evans’ research highlights a novel understanding of geometry within the thematic complex of the art and architecture of the Renaissance that emerged from discoveries in projective geometry and transcended to a drawing protocol with representational applications, but also as a medium for the geometric extraction of manufacturing information of challenging geometries. In analogy to these historical processes we can see similarities in the reception of computational geometry by architects from the mid-1990s up to today.

It appears that the pivotal contemporary role of mathematics, in our case a shift towards a topological understanding of geometry, is again responsible for an altered relationship between the designer and the designed. The created artefact is hereby not the fruit of artistic control with the defined preconceived result in mind, but rather a controlling of a relational geometric system through which a formal result emerges. Spuybroek writes: “We don’t design with curves, we just lay out relationships. And relating them makes things take on curvature, because that which relates creates the thing” (Spuybroek 2008, 165)

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Emerging variability in the design process Reading this process through an historical analogy can connect our practice to its predecessors. R. Evans’ research on the role of projective geometry distils the manner in which the relationship between the designer and its architecture has changed and what concepts had been introduced that were responsible for this shift. Evans argues that through the discovery of projective geometry—first in painting and later for architectural purposes—a conceptual barrier was broken that expanded the scope of the present Euclidian understanding within art and architecture once and for all.

Euclidian Geometry as described in the Elements dominated the perspective on geometry from its publication in around 300 B.C., and presents among other topics a set of ten logical axioms (five of them called postulates—including the parallel postulate—and five called axioms) that describe the defining principles for straight lines, circles and angles and the famous parallel postulate. Euclid’s parallel postulate defines: “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on the that side on which the angles are less than the two right angles” (Bonola and Carslaw 2007) The underlying mathematics is concrete in the sense that it gives clear instructions for how to create specified geometric objects, like e.g. spheres, using only a compass and an unmarked ruler. The practicality of this geometry can be seen in the guidance it offers for measurement by angle and distances, which was applied in such areas as land surveying and calculating the volume of solids. Given the fact that contemporary digital design tools and their geometries complement the repertoire of the architect, the final materialisation of the forms created in this way still takes place through a Euclidian geometry protocol. In his seminal text “A Plea for Euclid” Bernhard Cache addresses this aspect: “As far as architectural practice goes, we think that what has to be thought and drawn is the way in which we use, translate, or plunge multidimensional spaces of all kinds into 3D new Euclidean figures. Just as an example, I will mention that Objectile uses everyday mathematical functions with a great number of parameters in order to design 3D surfaces. We then work within multidimensional parametric spaces, although the output is plain Euclidean 3D. I would say that the essential part of our work is not to create ‘multidimensional topological non-Euclidean virtual spaces’ but to design interfaces between parametric hyperspaces and 3D Euclidean figures.” (Cache 1998) The development of a modern “non-Euclidian” geometry that underlies contemporary CAD-based tools sees its origins in an artistic quest for representation that is synchronised with the perception of the human senses exercised in the early perspective drawings, which opposed the Euclidian axioms in more than one case. The acquired understanding of perspective drawing methods led then to further expand its application as a revolutionary tool for the design and stereotomy of stone-vaulted structures developed by de L´Orme and Desargues, which was then transferred into a mathematical concept—projective geometry—developed by Lobatechvysky, Bolayi and later Gauss (Russell 1897, 7-8), (Preparata and Shamos 1985, 1-26).43 The initiation of a canonised projective geometry protocol that lay the foundations for a later topological conception of geometry started with an architectural and artistic problem—the visualisation of the world from an arbitrary viewpoint—that had been addressed by Alberti, Brunelleschi and Albrecht Dürer ( Dürer 2006) in the 15th century.

Long before Alberti and Brunelleschi several investigations had been conducted on the study of perspective, Euclid’s book Optics had defined the terminology of visual ray and the visual cone. Vitruv mentions the centre point in his ten books in the following manner: “Perspective is the method of sketching a front with the sides withdrawing into the background, the lines all meeting in the center of a circle” (Vitruv 1987).

For good insights into the historical interconnections between different geometric protocols and architecture and their contemporary software applications, see Cache (1998).

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Artists and architects, independent from each other, developed geometric methods and mechanical machines for the creation of perspective drawings that saw application, for instance, in the visionary tableaux of Renaissance ideal designs of urban scenarios. The applied geometry was centred on an investigation of conical and pyramidal figures and their sections. The tip of the cone represented the viewer’s eyes, which, in combination with the constructed horizon line, allowed a perception different than the orthographic projections known at the time. Following this method, parallel lines would meet at the vanishing point, a fact that would interfere with the Euclidian parallel postulate that two parallel lines never share a common intersection point.

Artists experimented with alterations of the horizon line and the related eye-point (or point of view) as shown in the pictorial description of the body of the dead Christ by A. Mantegna (Ill. 44), in which the eye-point and horizontal line are wilfully separated to allow a low-angle perspective.

Ill. 44 The Lamentation over the Dead Christ c. 1490 (Andrea Mantenga) on display at Pinacoteca di Brera, Milan

Through these early perspective studies, which had yet to be formulated in a fully abstracted mathematical description, an iconographic translation took place based on an artistic relation of viewpoint and horizon line. The artistic act of identifying a geometric position within an infinite range of potential viewpoints/horizon lines was the subject of experimentation, resulting in extreme applications like anamorphic projections that emphasised an iconographic concept through a calibrated artist’s perspective. In the latter the eye-point was placed outside the 115

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expected viewing position. The undistorted perception of the object could then be achieved only at a pre-defined location and would show a distorted representation of the subject from the normal viewing position. The choice of geometric construction was hereby conceptually driven and could—in the case of anamorphosis—encode the subject’s representation to become detectable only by the informed viewer.

One of the most prominent depictions of that extreme perspective is an anamorphic representation of a skull in the foreground of the painting “Die Gesandten” of 1533 by Hans Holbein der Jüngere, on display at the National Gallery in London. The skull can be perceived only if the viewer catches the viewpoint located close to the canvas, around 30cm to the left of the object.

David Lauer describes the conceptual implications of the perspective method for the relationship between the viewer and the viewed. It is only through movement and personal engagement that the encoded information becomes apparent. For a discussion on these topics and their philosophical implications by him and others see Cha and Rautzenberg (2008, 7-23, 230-245).

Alberto Peres-Gomes presents an in-depth investigation of the relationship between anamorphosis and architecture in his book Anamorphosis: An Annotated Bibliography: With Special Reference to Architectural Representation (PeresGomes 1996).44,45

Designing with geometric relationships This geometric investigation that was still taking place in the arts would soon be conceptualised for a broader application expanding into architecture and finally mathematics. At this moment in history a creative alteration of the described subject was taking place, that was centred not solely on the accurate description of its real measures as set out in Euclidian thinking, but also on an understanding that artistic concepts could be implemented if the relation between the depicted and the viewer were actively investigated in a geometric setup of visual multiplicities. Geometry shifted from mere representation of a single, Euclidian reality, towards a geometry of relations or “Géométrie de position” as described by Lazar Carnot (Carnot 1803) in the beginning of the 19th century. This shift, that lay the foundations of topology and projective geometry, was characterised by a geometric inspection of proportional relationships that would remain constant under a change in form. Such an investigation can be seen in the etchings “Les perspecteurs” by Abraham Bosse (Ill. 45 left), an abstracted illustration that depicts three noblemen in inspecting three equilateral squares from different height levels and angles, in which the relational properties between the different rays remain constant while the lengths of the lines connecting the eye and the corners of the squares located at the floor change.46

44 The intentional correlation between a geometric system and its iconographic content can also be seen in Piero del a Francesca’s work. Robin Evans gives a detailed account (R. Evans 2000, 123-179) on the relationship between the artist’s application of “another method,” an innovative perspective system and its translation in a series of artworks with scenographic compositions.

Evans explicitly mentions “The Flagellation of Christ” 1455-1460, on display at the Galleria Nazionale delle Marche in Urbino, Italy, which constructs an isolated depiction of a Christ figure by means of a perspective that centres on the three main characters in the foreground, who appear unaware of and undisturbed by the flagellation in the background.

45 In Claude Bragdon’s work of the early 1900s, two-dimensional projections of four-dimensional geometries represented a visualisation of a metaphysical world located beyond our human scope of perception. Bragdon integrated these geometries in his architecture for ornaments, wallpapers, lamps, etc. For information on his work and his distinct relationship between geometry and iconography, see Massey (2009), Bragdon (2005).

46 One can see a close relationship between the Abraham Bosse’s illustrations and Gérard Desargues’ later parameterisation in his famous theorem, which asserted that if two triangles are in perspective from a point, then they are also in perspective from a line..

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Ill. 45 “Les Perspecteurs” by Abraham Bosse (1647)47

At this precise point in time, geometry became a conceptual tool that would introduce potentials of variance and repetition into the later architectural design process. Designs were realised by contemplating the constructive conditions that would compose the final architectural solution. Geometry served as the intellectual vehicle through which individual concepts could be translated into the drawing process. This aspect was expanded further in the subsequent period through the integration of extractable manufacturing information, as will be shown later.

Traits, trompes and law curves The Renaissance man was a person of broad knowledge covering the fields of architecture, mathematics, philosophy and mechanics, as seen in the works and publications of, e.g., Albrecht Dürer and Piero de la Francesca among many others. Their awareness of the interconnections between the different disciplines, which were not formally segregated in their time, favoured a quick abstracted investigation of the underlying principles of the newly acquired visualisation tools from a mathematical perspective, and an extension towards an architectural application exploiting the innovative capabilities of stereotomy. Within a period of less than 100 years,48 the new geometric understanding matured from a mere a drawing method into a design tool for a new architectural typology with information that could be used for the process of building.

The first translation of a projective principle in an architecture manifesto was presented by Philibert de l´Orme in Le premier tome de l’architecture (1567).49 The book covered a broad range of architectural topics, like numerous publications in its time, ranging from concrete advice on financial and contractual issues (Book I Chapter IV: l`architecte et l´argent, Book I Chapter III: Relations avec l`architect et les comanditaires) to advice on architectural 47 A. Bosse’s illustrations can be found in the book Maniere universelle de M. Desargues por practique la perspective by Gerard Desargues (1647), which was published after his famous treatise “Brouillon project d’une atteinte aux événements des rencontres d’un cône avec un plan (1639),” which presented a mathematical translation of the abstracted principles of perspective construction into a geometric axiom: Desargues’ theorem.

48 If we consider Alberti’s De pintura (1435/1436) as the first instruction manual for the construction of perspectives, and Philibert de L´Ormes Le premier tome de l’architecture (1567) as an architectural expansion of its underlying principles of perspective construction.

49 See especially Book IV, chapter III. 117

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practice (Book I Chapter X: Necessité de faire plusieurs modèles) but also gave technical instructions for the creation of building components like windows, chimneys and portals.

One chapter in Le premier tome de l’architecture (1567) is dedicated to a geometrical construction based on projective properties that l´Orme had developed and applied in his own architectural projects. His innovation, which he called “le Trait,” described a method for the design and manufacture of a squinch and is an instrument for the geometric control of multiple connected masonry elements through a single drawing. In his method, which he used for his famous “Trompe d`Arnet” in the Chateau d`Arnet, the application of a central perspective point toward which the entire geometry of the overarching corner squinch is oriented, is apparent (Ill. 46). The proposed geometric system of the trait was described by De la Hire: “The workers call the science of the trait, when cutting the stone, the science that teaches how to cut and separately construct more than one ashlar of stone so that, when they are put together (at the right moment), they create a piece of handwork that can be considered as a single object.” (de La Hire 1596) in Trevisan (1999, 1). Trevisan adds: “The trait is therefore a diagram, usually drawn to scale, which allows us to solve real constructive problems connected to the structure and the cut of the ashlars of stone.” (Trevisan 1999, 1) The system that underlay the construction was confined by a series of “two-dimensional operations to display the principles of a new three dimensional method of representing space”. This geometric operation, called rabattement, “would fold different planes (usually a lateral and or a ground view) into a single plane.” (Veltman 1992). This controlling process would grant the architect an expanded design space that was coupled with precise stereotomic manufacturing information.

Trevisan explains this procedure as follows: “By means of rotation and overturning, starting from a plan and a vertical section, it is possible to define the height of each point of the construction and therefore the curve of intersection between the two surfaces in the two dimensions of the diagram. Furthermore, still following the same procedure, it is possible to construct the development boards (panneaux) of the inferior and superior surface of the vault and its front. In this way not only can development boards or plaster models be easily constructed but it is also possible to proceed operatively with the cutting of the stone ashlars. (Trevisan 1999, 1)

Ill. 46 Construction of the trait for the trompe d´Adnet in Trevisan (1999, 1)50

The protocol allowed the construction of complex vaulted structures that de L´Orme called “trompe”. A trompe can be described as a “splaying, conic surface of masonry, reminiscent of a trumpet, upon which projecting towers usually are supported” 50

For a detailed discussion on the Trait d´Adnet see also R. Evans (2000, 185).

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(R. Evans 2000, 181). “The trompe supports itself and wall works above it by placing the weight of the entire structure on the imposts.

This voute suspendue en l´air, as de L´Orme himself calls it, was built to support stairs or small cabinets (as in the case of the trompe of d´Adnet) without the necessity of resting on the floor; perhaps though, it was to give the whole structure a characteristic element.”

(Trevisan 1999, 10).

In the detailed reconstruction of the trompe d´Adnet by Trevisan, the author detects an interdependent geometric order of the main formgiving elements based on holy triangles and circles, which were used as a systematic design driver for the final shape.51 Trevisan summarises his geometric investigation as follows: “The use of the trait géométrique acts like a design lever on the building, multiplying the actions in an amazing chain reaction. Few lines, in this case two simple circle arches, regulate and define the entire architecture, transmitting all the characteristics, proportions and potential volumes by parthenogenesis. Indeed, the act of creative planning is found completely in the construction of the trait: it is an indirect action and it does not concern the object itself but its constructive sections.” (Trevisan 1999, 7).

Trevisan identifies a radical approach implemented in L`Orme’s system characterised by a parametric relationship between geometry and derived formal output that emerges from a strict, canonised action. The architectural form evolves out of a bottom-up geometric process that negotiates a variety of potential solutions by calibrating law curves or ruling geometric elements that are not part of the designed object themselves. This mathematical system alters the relationship between the architect and the designed object in such a way that a singular morphology emerges through the artistic calibration of these flexible geometric elements. Designing evolves as a fruit of a systematic process that renders the designed object through a constrained fixation within a set of infinite potentials.

In the following years de l´Orme’s invention was expanded in depth and greater abstraction for a more general application within stereotomy.

The mathematical core of the traits was centred on a geometric52 investigation of conical sections (ellipse, circle, hyperbola and parabola) and were mathematically elaborated by Desargues in his treatise “Brouillon project d’une atteinte aux événements des rencontres d’un cône avec un plan” (“Rough Draft of Attaining the Outcome of Intersecting a Cone with a Plane”) of 1639.

Desargues examined the relationship between points of conical sections, represented as two triangles, in which the corner points could be connected by a group of three lines (passing through the related corner points) that meet in a single point. The vector extension of the three lines would be the framework in which arbitrary triangular forms could be constructed that would share a property of invariant relations. Desargues, a mathematician and architect, immediately recognised the potential of his technique for use in broader masonry applications beyond the trompe. Within eight years Bosse and Desargues developed a comprehensive geometric guide for stereotomic fabrication, which they published in the book La Pratique du trait a Preuves de Mr. Desargues Lyonnois Pour la Coupe des Pierres en l’Architecture. (Bosse and Desargues 1643), that gave clear technical instructions on suitable typologies of these structures and their dependent geometries.

In a direct comparison of two trompes by Desargues and de l´Orme different design approaches become visible (Ill. 47). De l`Orme is fascinated by the control he acquires over a formal richness, which he cultivates through the freeflowing edge curves of the trompe and connects with his natural iconography, as is apparent in many passages of his treatise. The drawing itself is constructed with multiple vanishing points, leading to a distorted representation of the architecture. Desargues, in contrast, places a centre point in the middle of the illustration and draws a technically perfect representation of the evolving geometry with a more disciplined course of the trompe’s seams.

The author revises some of Robin Evans’ geometric considerations as regards the implementation of the elliptical conical section that shaped the vault.

52 Contrary to Descartes’ approach, which investigated solutions of conical sections derived from analysis.

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Ill. 47 Drawings of trompes by Desargues (left) (Desargues and Bosse 1653, p79), de l`Orme (right) (de L´Orme 1567, 196)

Desargues’ reason for executing the edge line in such a manner lay potentially in his desire to demonstrate a mathematical concept rather than to expose its design potential. De l `Orme’s treatise, on the other hand, covers a wide range of common architectural problems and gives practical guidance for geometrically induced design processes, but also provides additional insight into the architect’s underlying fascination with nature as the locus for an architectural language that embraced natural sciences to enhance artistic expressivity.

De l `Orme contemplates his relationship to geometry in his own words: “I freely confess that I never had a taste for study or research either in physics or geometry except in so far as they could serve as a means of arriving at some sort of knowledge of the proximate causes … for the good and convenience of life, in maintaining health, in the practice of some art … having observed that a good part of the arts is based on geometry, among others the cutting of stones in architecture, that of sundials, that of perspective in particular.” In Tyler and Bicelow (1939, 317) The architectural expression of the two trompes varies within a communal geometric system and potentially reflects the designer’s conceptual intention. The adequate spatial constellation of its discrete members, in our case the course of the vectors that all share the same centre point, concretises a potentially infinite bandwidth of possible solutions through articulated design intent. Similar to Bosse’s illustration of the three noblemen, the object itself is a composite of its inscribed geometric relations, defining the final position of the formgiving levers and their resolving geometry.

The obvious impact of a more scientific approach towards architectural design manifested in these works later translated into larger architecture in the works of Guarino Guarini and others who were influenced by a projective approach to geometry.

In the design of the dome of the SS. Sindone Giovanni in Turin by Guarino Guarini of 1680, the architect explicitly references Desargues’ publication as inspiration. Guarini’s commission consisted of a renovation of an existing dome and a new design of a cupola structure that forms the centre of the church. The cupola is shaped like a cone in which the sculptural relief and openings are derived from a projective process (Ill. 48) that creates a horizontal and vertical connectivity between the individual members.

Elwin Robison describes: “These arches, together with the broad pendentives that they frame, form a zone of transition terminated by a large circular cornice, upon which Guarini set the drum, with six tall, arched windows, and the dome of the 120

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chapel. The dome is formed of six sets of six elliptically arched ribs, each set tracing a regular hexagon in plan. Each succeeding hexagon of ribs is rotated thirty degrees with respect to the lower hexagon, so that its elliptical ribs spring from the keystones of the preceding tier.” (Robison 1991, 385 ff)

Ill. 48 Left: cupola of S. Sindone, right: projective construction of the cupola’s windows and ribs (Robison, 1991)

Guarini’s construction is based entirely on a geometric system of projections that dominate the individual element and apply projective transformations onto the discrete ornaments that act as load-bearing members to heighten the perspective appearance.

Along with the projection of the perspective rays comes a vertical rotation that constructs the rhythm of the openings. The individual window is defined by the intersections of the vectors through the cone’s inner surface. Guarini’s design method gives the structure an appearance of modernity since it replaces the traditional interiors of cupolas, often constructed as regular cassettes, with an enhanced spatiality derived from the circular rotation of the individual rings. Robison stresses the importance of light, which complements the materiality to enhance the perspective effect. Robison writes “Nevertheless, he retained large windows between the ribs, producing the strong backlighting that visually erodes the structure and makes it appear ethereal.”

(Robison 1991, 387) This thinking in variation and dependencies overruled the century-old Vitruvian ideal of architectural design for a period and paved the way for rational and functional theories developed by Claude Perrault (Perrault 1683), JeanNicholas-Louis Durand (Durrand 1802-1805) and Eugène-Emmanuel Violett le Duc (Viollet-le-Duc 1871). Design practice shifted for a limited period from a contemplation of proportions and pre-defined structural order to a systematic experimental practice.

The history of architectural design development is anything but linear. The developments in architectural geometry that appeared in the late 1600s and thereafter did not become a permanent and practiced part of the design process of architects in subsequent years, but fell into oblivion until much later, although the technological understanding of these protocols was readily available and well documented. Bernard Cache investigates this question in a paper on the obvious indifference of Gottfried Semper towards projective geometry in favour of a neo-Euclidian practice of geometry. His neglect of the available geometric protocol is especially remarkable since Semper was a pupil of Gauss, who first rejected Euclid’s 5th postulate, while Semper’s conception of textiles that “anticipates topology and knot theory” points to projective geometry as a logical approach (Cache 2006, 55).

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Summary The practice of projective geometry delivered a flexible design interface for the artist and the architect, which jettisoned the singular view of Euclidian geometry in favour of a geometric protocol that embraced variance and alterations. This constructive process was determined by a personal perspective and individual interaction initiated by the pictorial approaches of Alberti and Borromini and others. Geometry became the transmitter of the individual design concept by determining the implementation of its confining elements. The Euclidian approach focused on the object and its properties, whereas projective thinking introduced variability and process. The individual perspective of the artist was geometrically projected to the viewer and guided his mode of perception. The design protocol would resolve in creations by holding fast the shared relational constraints that remain invariant under transformations and providing an abstracted conception of a design process as a field of infinite potentials.

Along with the geometric protocol came an altered role of the architectural drawing, which was now employed not solely for the depiction of an architectural design, but included relevant fabrication information that could be extracted from an interwoven geometric process. Through this geometric method the drawing’s function was transformed from visualisation to fabrication. The employed material and fabrication methods were respected in the overall shape of the evolving geometries that would promote a distribution of stress forces and integration of the stonemason’s manufacturing constraints.

In this route of historical geometrical developments within the arts and architecture, a persistency of properties is observed, part of which reappears in contemporary CAD-driven design and manufacturing tools. These aspects will help to investigate the contemporary conception of a design protocol with further developed design tools and a stronger relationship to the manufacturing of architecture created using this technology.

The characteristic changes brought by the introduction of projective geometry to the architectural design process affected three main aspects.

I.

Design Process a. Introduction of variance and alteration b. Indirect design process c. Design emerges through a fixation of flexible geometric entities within a conceptually defined position

II.

Instruction a. Coupling of representation and fabrication information within a single drawing format b. Integration of material constraints in the drawing format

III.

Typology a. Development of a distinct tectonics through a geometric process

The abstracted analysis and structure of this historical proto-parametric design protocol reveals parallels to the contemporary role digital design tools occupy in architecture. The classification of the different fields in which conceptual and processural changes took place appears to mirror a contemporary design process. Through this 122

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unfolding of a historical process, a denser web of architectural references can be woven that allows a correspondence between historical and contemporary research. This specific viewpoint is grounded in an interpretation of scientific development that is informed by historical analogies and references that affect our thinking today. Yet it has to remain an endeavour with a personally biased reinterpretation of history through our contemporary perspective. “To remember the past is to reconstruct a former presence, now distortedly seen, from the point of a more immediate present. Regardless of the imposed transformations, the past remains firmly embedded in objects made. The record they hold remains precise and accurate, autonomous from any later fabrications of meaning.� (Scofidio 1988, 41)

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4.3.2 Digital design and material performance The portrayed historical design process was confined by a virtual multiplicity of potential solutions constrained by the protocol of the trait, which required a local determination of the boundary conditions by the architect before a shape could evolve. The realisation of the thus created artefacts was aligned with the spatial conditions and the manufacturing process with regard to sizing the elements and to the available instruments for stone cutting that allowed the measured geometries to be fabricated on the building site.53 In juxtaposing this historical process with the envisioned research in digital design that actively integrates material properties (Ill. 49), one can identify the following altered roles that fall to geometric construction and materials.

Ill. 49 Comparison between trait and digital material model

The proposed workflow shows several differences from the trait model with regard to implementable information that drives the formation of the digital model, and to the role of the material in the final morphology. In the digital workflow proposed here the final artefact evolves out of a composite performance between digital and analogue properties, and not as the result of a geometric calibration of its isotropic properties, which remain largely invariant after the construction has taken place. Through its structural and material properties the material computes the given Desargues gives clear instructions to the stonemason for cutting his geometries in his book, defining a process chain from design to manufacturing. See Desargues and Bosse (1653, PL 4, 8, 9, 10, 11).

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digital model, composing the final morphology in a dependent interaction. The trait, on the other hand, integrated the material and fabrication properties in a more detached manner, identifying the basic load-bearing geometry and distribution of the joints with regard to their dimensions in stone.

Relational design Digital tools now define a different protocol for steering architectural design activity that often opposes a transparent formal preconception of the object through processural complexity and employed graphical interfaces. The first generation of digital architects experimented with computationally induced geometric variation driven by the boundary conditions of available animation software. The fascination of these early experimental investigations centred on the conceptual and morphological properties that would illustrate this procedural set-up, which went beyond previous digital drawing tools that were limited to translating an analogue drawing process to the digital realm (Terrien 2005). Aspects of time, movement, program and interaction (Spuybroek 1997) were implemented into the generated form through a process in which “numerical parameters can be keyframed and dynamically linked to alter the shape of the object.” (Lynn 1999, 24-25). The design engagement of the architect would lie in the implementation of these abstract properties through inverse kinematics networks, warp forces and particles (Lynn 1999, 30) that would computationally unfold in a unique geometric expression over time.

Computational processes that follow the first generation of digital tools investigate—among others54—emergent (Hensel and Menges 2004), (DeLanda 2002) and associative parametric design software (M. Burry 2003), (Aish and Woodbury 2005), (Kolarevic and Malkawi 2005) in which local rules constrain parametric relations or fitness functions that unfold into geometric form with varying degrees of preconception of the emerging design. The control of the design is achieved by tuning recursive sets of interdependent reactive systematic entities that agglomerate into a joint final morphology far removed from an assembly of individual discrete objects. The element’s relationships implement material and ecological implications or manufacturing constraints, among other factors. Recent years have seen complementary research streams focusing on, for instance, the coupling of digital fabrication and design modelling (Shelden 2005), (Kolarevic and Klinger 2008), geometric optimisation (Pottmann, Brell-Cokcan and Wallner 2007), (Liu, Pottmann and Wang 2006), digital ornamentation (Strehlke 2008), (Del Campo and Manninger 2008) and methodological research (Kilian 2006) (Schoch 2005), (Holzer 2009).

The evolving architectural design process has not become more linear, but is still bound to make “inspired decisions with incomplete information” and has to “anticipate the consequences of the making or doing” (Aish 2005) along a path that requires constant adjustments and corrections. Several entangled layers of geometrical and non-geometrical contents emerge in an asymmetric timeline during the process and are responsible for changing pre-conceptions of the emerging architectural result. Competing issues, like programs, environmental and economic performance, but also less obvious entities like the individual design strategy, comprise the process of digital formgiving and must be merged into a coherent systematic envelope. Non-geometric issues have to be morphed into a coded identification of associative relations and interacting entities along with the given boundary conditions of more concrete character, like site and program. The geometry machine that is constructed by these interwoven relationships channels, dynamically interprets and changes these organic fields of information that substantially drive the design intention.

54

For a good overview of contemporary digital design techniques see R. Oxman (2006).

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Implementing material properties In recent years a stronger relation between digital and physical practice has emerged, which abandons a purely computational approach towards design in favour of interaction between analogue and digital properties during the design phase (Spuybroek 2004) and for architectural construction. Recent research by Gramazio and Kohler (2010) Tamke et al. (2011), Knippers (2011), Ahlquist and Menges (2011) Hernández and Gengnagel (2011), P. Block (2009) and others is centred on the integration of material properties under manufacturing constraints that inform a digital tectonics through activating a material’s inherent structural performance potential.

In the case of this year’s ICD Pavilion by Achim Menges the morphology of the pavilion design is composed by an analysis of the bending momentum of thin plywood sheets that supply the building’s skin and structural system through a parametric model that orchestrates fabrication instructions, assembly and manufacturing constraints. This process engages “the physical behaviour and material characteristics” (Institute for Computational Design ICD 2010) and utilises standard 6.5-mm wood panelling and subtractive manufacturing procedures in its realisation. Once the bending momentum of the selected wood panelling has been identified, a subsequent constrained design process can be initiated that identifies suitable manufacturing processes and joinery solutions for the individual elements. The material’s structural properties are utilised to stress the individual panels by the applied bending momentum that locks the joinery between individual elements. The research integrates fabrication and structural properties of varying materials into the design process, which, when assembled, activate an inherent property that was digitally conceptualised, tested and approximated to allow a relatively accurate preconception of a stable design in structural equilibrium.

In a recent PhD by Neri Oxman (N. Oxman 2010) the author investigates a design approach that computationally balances performance criteria, formfinding methods and graded materiality with a biomorphic perspective in multiple models and represents the first compendium in that format. The developed design space promotes a locus for an enhanced sensitivity of interaction between the digitally calibrated physical medium and its user or viewer by calibrating a material distribution that incorporates structural efficiency, formal richness and aesthetic qualities. The optimistic architectural promise at stake in Oxman’s work envisions an individual and sensuous architecture that takes advantage of the existing possibilities of mass customisation and biologically inspired geometric specifications to develop a new synthetic materiality. Oxman sketches computational workflows and employs additive and subtractive fabrication technologies that differ from those presented here and encourage future research in this direction. The conducted investigation is broad in its scope and addresses aspects of computational and biological formfinding, but also files a patent application for a variable-property rapid prototyping device.55 Research by Ramsgard-Thomsen and Karmon (2009) integrates computational tools that drive the composition of technically woven and knitted textiles that unfold their encoded behaviour through an interaction between structure and material. This approach is in this sense different from previous research, since the evolving morphology is flexible, yet inherently constrained by material properties and patterning information and collapses into momentary states of equilibria. These morphologies are infinitely variant but not arbitrary since they obey the tectonic connectivity given by the structural assembly and the fabrication material employed.

55 The research presented here investigates the topic not from a distinct biomorphic perspective of enhanced functionality through heterogeneous material distribution and additive fabrication, but rather from a processural angle that identifies “intensive” properties that are inscribed in the fabrication tectonics and geometric conditions, which allow adaptivity to technological progress but also conceptual exploitation of its inherent properties for a new formal language and design process.

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“Our research concentrates on the design of highly specified membranes that incorporate computational as well as structural performances. Our work explores the collapse of sensing, actuation and structure into one integrated membrane.” (RamsgardThomsen and Karmon 2009, 4) Form here is not identical with a preconceived image of a fixed design that materialises the end of a creative process, but rather a dynamic field of characteristic tectonic potentials that read the environmental or performative conditions. Constrained assembly conditions given by the textile properties and their local formation actualise into temporal formations through homeomorphic translations. Design cannot be pre-conceived as such but migrates dynamically under the given constraints if an external change alters its boundaries. Form thus exists as actual and virtual potentials that grant a temporal identity driven by multiplicities inscribed in the chosen material and structural tectonics. This geometric set-up now can be coupled with properties derived from additive fabrication processes that drive a characteristic form from a material-derived stance and whose properties can be adjusted.

Form and material relations Additive fabrication and digital design can allow the tuning and fabrication of the structural and/or mechanical composition of materials. This aspect challenges a historical architectural understanding of the relationship between built form and employed material that has been investigated in the past by Aristotle, Scamozzi, Violet-le-Duc and L. Kahn, among others. Material, form and geometry are now intrinsically interwoven and can unfold a unique morphology each time their boundary conditions are altered. In contrast to an historical conception of material whose properties and applications are known through experience, an additively fabricated material is defined by locality and uniqueness and uniquely tailored in structure and composition to a performative domain.

In additive fabrication, the identifiable character of form emerges not from a deterministic pre-conception of the designed artefact, but through a complex interaction of all formgiving instances. Ramsgaard-Thomsen’s research in the field of computationally controlled textiles can help to gain an understanding of a novel conception of a tectonic language that can arise from such controllable materiality. In contrast to the historical trait in which the design protocol calibrated a desired geometric output, such an approach can identify only a structural and material domain of potentials and facilitate the emergence of characteristic variability and complexity that evades a direct mapping of cause and effect in the design.

The conception of such structures has to synthetise and analyse the design-driving entities. Synthesis hereby operates under the presumption that the functioning whole can be explained through the mechanical behaviour of its components. The anatomy of each individual member and its contribution to integral performance are dissected to yield a theory of overall functionality. In analytical thinking, the focus of the observation lies in the description of the performance achieved without any clearly defined knowledge of its interacting parts.

“The terms analysis and synthesis come from (classical) Greek and mean literally ‘to loosen up’ and ‘to put together’ respectively. These terms are used within most modern scientific disciplines—from mathematics and logic to economy and psychology—to denote similar investigative procedures. In general, analysis is defined as the procedure by which we break down an intellectual or substantial whole into parts or components. Synthesis is defined as the opposite procedure: to combine separate elements or components in order to form a coherent whole.” (Richey 1996, 1) “But we cannot attempt to draw conclusions about how the system functions, if sufficient knowledge concerning its internal properties is not available to us. We must, instead, invert the process: we need some kind of theoretical framework within which

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we can first draw conclusions about the system’s internal properties. And in order to do this, we must analyze the problem that the system must solve in order for it to accomplish what it does.” (Richey 1996, 14) In synthesis the creator is aware of the behaviour of each individual member in the formation process. He is granted permanent control over the entire process, while an analytical approach is based on a holistic experience of the resulting design under specific local conditions. The concepts are not viewed as necessarily rivalling methods in the context described here, but as complementary approaches that integrate computational preconception and memory in the perception of fabricated artefacts. An experience of these designs is based on an analytical understanding of the discrete elements that compose its overall assembly—in our case, a definition of cellular elements and their topological or structural ordering principles—and the experience of the overall structure. The space between these two perspectives comprises a domain in which a conceptually encoded performance of the local element is interpreted through dynamic material engagement.

The morphology of such structures emerges from a space of potential formations that actualise and become metric in a dynamic process.56 Through the calibration of the material’s transformative potentials that vary by their degree of freedom, a formal richness and variability can emerge through interaction with external formgiving factors. The intensities that confine a characteristic dynamic or morphological domain beyond scale are actualised through their transfer to metrical space and its encompassing environmental conditions. These properties allow an inspection of created structures through a process of both synthesis and analysis that integrates the local and the global conditions and can help to outline the decisive design parameters. The described topological properties of computational design tools thus appear suitable to place relational constraints on the local or systemic level, prior to their integration into a metric environment to calibrate the distinct degrees of freedom of the discrete elements. The calibration of the topological properties renders a characteristic tectonics extending across of state of momentary equilibrium.

4.3.3 Critical summary From the research presented here several aspects can be summarised that are relevant for conceptualisation of a design protocol that integrates computational and material properties in a novel fashion. A mirroring between shared properties of historical and recent architectural developments, both of which brought radical technological innovation in the field of design, fabrication and typologies, has the potential to point out processural characteristics of future design processes, some of which will be experimentally investigated here.

From the drawn to the instruction The protocol of the trait connected representation and fabrication in a novel format that was unprecedented in its day. According to this protocol, the drawing extracted manufacturing information from a challenging innovative geometric typology that was adapted to what the involved craftsmen required. The trait defined a precisely developed geometrical protocol that was actualised through integration to site conditions.

In the technological developments of recent decades, this aspect was amplified further through an initial understanding of architectural formgiving that allowed a temporary supremacy of the modelling system over a preconceived form. Animation software possibilities introduced a formgiving timeline into the creation of a Manuel Delanda’s text on “The Mathematics of the Virtual: Manifolds, Vector Fields and Transformation Groups” (Delanda 2002, 9-56) provides an in-depth explanation of the mathematical foundations for understanding this complex performative interaction between discrete entities, movement and emergent morphologies.

56

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morphological result that shifted the design process more toward the calibration of systematic boundary conditions and away from the explicit design of the final object.

In later years the systematic approach was coupled with a combination of digital modelling and numerically controlled fabrication technology. The digital information extracted from three-dimensional models and drawings directly informed the computationally controlled fabrication unit. The created model implemented information from many formgiving instances and media including analysis and simulation data, behavioural rules and graphical interfaces. The embedding of these external drivers through translation into a geometric system expanded a contemporary notion of the relation between the drawn and the fabricated by blending multiple morphological drivers that constrain the designed form. It is expected that in the coming years this aspect will be further differentiated through computational solutions for material design, increased usability of parametric and generative modelling software, and a stronger bonding of analysis and the design process under environmental and structural aspects that can be fabricated directly.

Emergent typologies Selected architects’ embrace of the projective geometry protocol led to the development of a novel building tectonics for vaulted structures that evolved from experimental investigations of its formal potentials. The geometric protocol was utilised here not as a complement to the classical set of drawing methods, but was implemented actively to foster designs of formal autonomy and character.

In recent developments in computational geometry for architecture, which investigate a design process that interweaves material properties, digital design and fabrication, we find interesting analogies that pave the way for novel tectonic systems and formal languages. Through a calibration of material properties and the fabrication of such this development can be further enhanced and allow the emergence of building components with interesting dynamic or multi-functional properties in a novel assembly system. Performative complexity is then achieved not by complex mechanical assemblies, but through locally differentiated materials. Through integration of the characteristic benefits of additive fabrication, an autonomous and novel tectonic language can evolve that cannot be produced by alternative methods. As stated before, the potentials of additive fabrication lie in fostering these properties, alone or in combination with related technologies, rather than in competing with well-established conventional manufacturing workflows.

Relationship between the design and process The trait introduced formgiving levers as part of the design process that would echo their configuration in the final design although not appearing in the resulting shape. The process this initiated separated design activity from the direct definition of appearance, but introduced a separation from the drawn and the object that was connected through the drawing process. This design process was nevertheless guided by an idea of formal prediction, but allowed formal complexity to emerge through a novel drawing interface.

The shift in computational design that investigated procedural design concepts extended this approach through a higher degree of detachment from the predictability of form. Computational models of emergent behaviour do not allow an a priori conception of a design that occupies the end point of such a process, but establish their own process-dependent formal language. Interweaving the design with complex material performances that interact with this generically digital tectonics differentiates this process even further. A new perspective must be taken on the 129

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formal description of fabricated artefacts that can emerge through a coupled performance of both digital and analogue properties. Form is perceived not as static materialisation, but rather as a dynamic domain with characteristic properties that are activated through the material engaging with its environment. The conceptual understanding of these design processes have to utilise synthesis and analysis alike to gain an understanding of the formgiving processes at work. Despite the complexity of material performance created in this way, which could potentially elude a reductionist understanding of its functionality, successful design strategies can be developed in fair approximation through coupling digital and physical analysis methods. This domain of performance, on the other hand, can provide a novel locus for design and artistic activity in which the impact of abstract formgiving drivers are negotiated through structural performance into a distinct formal language that is less determined yet characteristic.

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Experiment I: Graded Auxetic Structures

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5.1.0 Introduction The experimental research investigates applications of additive fabrication and computational processes for control over tuned material behaviour through structural variation of the material tectonics. The projected performance of such material can affect its mechanical properties like elasticity or elongation, but can also provide for spatial expansion or compression through the control over its internal structure. The geometric calibration and fabrication of the latter can include varying degrees of bilateral and trilateral material extension. Fabricated with a conventional manufacturing option, a complex system would be required for the actuation and achievement of the desired performance; now this performance can be triggered by a bespoke material’s structure.

The literature review has pointed out a distinct class of auxetic materials that bear surprising form-changing potential in all axes that can be prompted through the application of stress or strain forces, which has started to see applications in mechanical engineering. Existing specimens that have been fabricated with 1D, 2D and 3D auxetic cells have relied on a mechanical process compressing polymeric foams, like in the examples of additively fabricated one- and two-dimensional auxetic honeycomb structures documented in section 4.1.2 Auxetic materials. So far all samples have utilised a periodic array of auxetic cells, yet a gradual alteration of the cell geometry appears achievable.

The creation of auxetic structures with a varying distribution of negative and positive Poisson values would expand the scope of available bespoke material performance, assigning local control over unilateral, bilateral and trilateral compression and expansion.

Dynamic form-changing potential that could be fabricated in such a manner without complex mechanical assemblies would facilitate architectural applications through a simpler construction process and grant a new locus for interactive performativity driven by simple steering mechanisms. The modelling process that composes a printable volume out of surfaces and dependent line-elements provides an accessible interface to subtly alter the spatial configuration of the individual components in such a manner that graded auxetic performance becomes feasible.

Each auxetic cell can be controlled numerically and spatially to show more or fewer re-entrant properties through the encoded positioning of the ligaments in their x and y-coordinates for 1D and 2D patterns, and x, y and z-coordinates for 3D auxetic nodal elements. In the research proposed here the local calibration of the inscribed form-changing potential can be defined by numerical values organised in spreadsheet data. This open interface allows the implementation of data sets deriving from many other sources that merely have to be translated to the spreadsheet format and its boundary conditions. The translation of visual, performative or other information into numerical matrices and the fabrication of such a material with form-changing potential would allow the interpretation of the initial formgiving parameters as movement potentials that can be activated and experienced in the material itself.

This contribution, which appears feasible with the coupling of digital design and additive fabrication, represents a novel contribution to the expressivity of building materials and their dependent integration into architectural formgiving.

The three experiments that will be conducted in this chapter will study a material inherent form-changing potential in one, two and three dimensions through an assortment of suitable auxetic cells that are parameterised from existing research. The three tests will gradually vary the auxetic properties within the individual clusters and monitor their mechanical performance. Specifically, three-dimensional auxetic structures pose a challenge for conventional manufacturing methods and hence point to additive fabrication’s potentials to enrich the scope of achievable manufacturing options and their distinct typologies.

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Employed testing devices The printed 1D, 2D and 3D specimens will be tested under stress and strain forces to trigger the auxetic material performance. For this purpose two testing gauges (Ill. 52) will be constructed that measure the deformation of the tensioned materials in all three axes. Through evenly spaced markers placed in the longitudinal axis along the material sample, deformation behaviour can be tracked between stressed and unstressed conditions. Ideally, different degrees of re-entrance would be achieved by the cells as they unfold completely at different points in time during the unfolding process, and the Poisson ratio would gradually shift from negative to positive when the pulling force is exerted (Ill. 50). To transfer the deformation values, a test sheet was developed on which the mechanical deformations under stress and strain could be recorded. Each test sheet contains the position of the unstressed or strained material and a minimum of two different stages of deformation that are retrieved from the mechanical testing procedure.

Ill. 50 Poisson value alterations under continuous lateral stress after full unfolding of the re-entrant ligament elements

Testing gauge for stress forces To examine the material’s behaviour under stress, a device (bottom) is constructed consisting of a testing bed and two U-shaped lateral profiles that house the material. The device is based on Rehme and Emmelmann’s test set-up that correlates applied stress and the sample’s expansion for periodic auxetic structures fabricated with selective laser melting.

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Ill. 51 Testing gauge by Rehme and Emmelmann (2009, 131-132)

In the device proposed here (Ill. 52 bottom) one profile is fixed onto the base plate with a wooden bar, whereas the other is moveable in the longitudinal direction and contained a scale that measures the path length of compression.

After maximum compression of the material is achieved and the compressive profile locked into position, the longitudinal and lateral deformation of the markers could be measured in their positions along the x and y-axes for 1D and 2D auxetic materials and along the x, y and z-axes for the 3D auxetic knot.

Testing gauge for strain forces For testing the material under strain forces, an initial device was designed (Ill. 52 top) that operated by pulling threads under tension. One side of the specimen was fixed in the gauge, and the other subjected to strain through a series of neoprene-padded threads placed around a guide bar and locked into position by a steel rod resting on a series of evenly spaced L-shaped hooks to fix the structure’s position. Once the structure achieved its maximum extension, the x, y and z-coordinates of the markers were read and diagrammed to study the characteristic differences between the different specimens.

In the course of the experiments, the developed gauge appeared unsuitable to measure the mechanical properties of the test samples. Even under their own weight the 1D and 2D polymeric material specimens showed critical deterioration behaviour around the padded rings; if continued, destruction of the strained edge seams would have resulted. For this reason an altered version of the stress gauge was developed (Ill. 53 ) to exert the forces on the specimen over a broader impact area. During the testing process one lateral edge was fixed, while the corresponding side was subjected to strain and arrested in position through bar clamps fixing the testing bed, the specimen and a wooden profile in the dimensions of 5 cm x 5 cm. Through the broader impact area the pressure exerted on the material could be lowered and mechanical failure prevented. After fixation the extension values of the markers could be transferred to the test sheet.

This critical mechanical behaviour under strain forces has to be integrated in the planning process of building components shaped in this way. A favourable activation method for such materials would have to devise a broad contact area that would be connected to the mechanical steering device and distribute the strain forces occurring away from the individual ligaments and towards the surface area of the specimen.

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Ill. 52 Top: initial testing apparatus for strain forces, bottom: testing apparatus for stress forces

Ill. 53 Revised version of the strain gauge

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5.1.1 One-dimensionally graded auxetics The first experiment will create a one-dimensionally graded quasi-auxetic structure with a maximum Poisson ratio of zero. This test will use a modified bow-tie cellular auxetic component developed by Bubert et al. in 200857 to study a one-dimensionally graded elongation process of a honeycomb-like structure. The known cellular element will be modified by encoded behaviour of the internal ligament pair that affects the bending angle and is thus responsible for the cell’s degree of re-entrance (Ill. 54). The designed structure shows a one-dimensional translation characteristic and hereby creates varying positive Poisson values throughout the lateral expansion of the sample. The sample has dimensions of 39 cm (length) x 15 cm (width) x 1.0 cm (height) (Ill. 55). The design of the individual cell is configured to comply with the boundary conditions of additive fabrication technologies, with a minimum ligament dimension of 2mm.

Ill. 54 Encoded transformation of the re-entrant ligament with a Poisson ratio of zero

Envisioned experimental outcome The experiment should develop a structure with graded longitudinal extension achieved by encoding a desired performance profile in the cellular geometries. The material can have specified extension values in the individual lateral sections that can be controlled via parametric modelling techniques. A modelling system for such structures consists of a lattice structure and a spreadsheet with numerical values that identify the envisioned distribution of the mechanical performance. The individual cells of the lattice structure integrate the respective values to position the ligaments within a constrained range that defines the maximum and minimum extensions of the cell (Ill. 55). The fabricated specimen would contain the maximum re-entrant cells in the centre of the sample and would gradually decrease the degree of re-entrance towards the edges. Cellular distribution can be organised along the U and Vcoordinates of the surface and also allows the creation of freeform surfaces to be populated by auxetic cells with

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See section 4.1.3 Two-dimensional auxetic structures: Re-entrant bow-tie structure.

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varying Poisson values. In a future application, each of these lateral strips could be responsible for a partial functionality that corresponds with the extension ratio.

Ill. 55 Top: design of the cellular element, bottom: geometric set-up of the test specimen

Known limitations Several restrictions apply for the design of structures shaped in this way. Since each individual cell is dependent on the re-entrance of the prior cellular value, the design has to implement the unfolding values of these cells to negotiate the final position of their lateral extension. The experiment has to ensure that all cells can be unfolded completely and reach their final state. Since different re-entrant states of the cells are imagined, the distinct points of complete unfolding vary. When a full unfolding of the ligament has been achieved and the lateral stress is maintained, a shift from a negative to a positive Poisson ratio can be expected, the intensities of which rely on the mechanical properties of the employed printing material. The assortment of the cells must be organised such that the shift from highly reentrant cells to neutral or positive Poisson ratio components takes place gradually, since encapsulated elements with high re-entrant ligaments can be blocked, preventing complete unfolding and hence the manifestation of the auxetic property. The behaviour of such structures is therefore based not only on the cell design, but also negotiates the 137

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material’s mechanical properties in different time-based intensities. The research will document this behaviour and analyse the material’s performance for potential parameterisation. The experiment will construct a sample with 1D gradual linear translation (Ill. 56) that increases the re-entrance values and allows a fairly accurate comparison between the envisioned performance profile of the lateral extension and physical output.

Ill. 56 Implementation of the physical test sample

Testing the sample The experiment will test the performance by analysing the graded longitudinal extension and compression with the two testing gauges that should force the individual ligaments to occupy their maximum unfolded and re-entrant states. The design process correlates the longitudinal extension with the individual structures’ values of re-entrance (Ill. 57) and identifies marker-specific behaviour in one axis. Since all three specimens undergo identical testing scenarios, comparisons between 1D, 2D and 3D auxetic cells can be made and correlated to the shape of the distinct cellular geometry.

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Ill. 57 Extension diagram of re-entrant ligaments

The sample is equipped with physical markers that indicate the longitudinal extension of the cellular array (Ill. 57).

The experiment then measures the position of the individual markers, which should indicate varying lateral extensions.

Fabrication The prints are fabricated using a Connex 500 printer by Objet geometries Inc. equipped with the Digital Material TangoBlack with a Shore A value of 61 (Ill. 58). The build direction of the sample is perpendicular in the z-direction to the cellular orientation of x and y-axes described above.

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Ill. 58 Connex print of 1D graded auxetic knot structure

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Analysis of stress and strain behaviour General performance The material was placed in the testing gauge and subjected to pressure with three different increasing compression loads (Ill. 59) that shortened the overall length of the structure by 2.5 cm. In the course of testing a sequential lateral bending movement could be observed in the centre areas that contained the bow-tie cells exhibiting the strongest indenting reaction. With increasing loads the specimen would show growing three-dimensional deformation that would form an arch-like course similar to a honeycomb (Ill. 60).

Ill. 59 1D auxetic structure—left: unstressed, right: stressed

This performance would gradually increase from the lateral edges inwards, suggesting a correlation with the cellular geometry and its degree of re-entrance. To map the deformation of each individual marker position the specimen had to be pressed down vertically onto the testing bed. Although the specimen had been fabricated with the elastic TangoBlack material, the dense array of cells with a ligament dimension of 2mm showed robust resistance to the stress applied. In contrast to the test by Bubert, which contained only a limited number of 1D auxetic cells (10 x 10 cells with a max. length of 35 cm), the sample fabricated here was modelled with a dense array of cellular elements (50 x 10 cells with a max. length of 39 cm). This altered ratio of performance spaces per cell and material dimensions yielded stiffer mechanical behaviour of the material and reduced reactivity to the applied force with regard to longitudinally controlled movement. The correlation of movement potential and fabrication appears to be defined by 141

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the scale of the individual cell and its required structural dimensions. This aspect of scale that dominates the performativity of the material is therefore of vital importance. In growing fabrication scales the correlation between ligament dimensions and cellular sizing can be optimised, granting a larger area of re-entrance or unfolding since the minimal material thickness remains smaller while the overall dimensions of the specimen can grow. The specimens produced here suffer from the rigidity of a structure constrained by fabrication parameters. On the other hand, the observed bending performance avails itself of the chosen dimensionality of the geometry to produce a resilient structure that unfolds through a simple mechanism. The experiment thus delivers two individual findings under bilateral compression: a.

For the creation of varying longitudinal extension the material structure, especially the ligament dimensions and cellular sizing, is crucial. Thinner walls and larger cells reduce the tension within the material and facilitate planar deformation. Alternatively, the utilisation of print materials with lower Shore A values like TangoBlackPlus (Shore A 27) reduce the tensile strength and allow for better folding performance at the price of more flexibility and less rigidity.

b. The chosen material dimensions appeared well suited to create a material with bending performance that can generate a curved shell out of the planar material. The curved, three-dimensional deformations that follow the degree of re-entrance produce a rigid arch-like structure through a simple activation method triggered by two wooden bars under stress. Further experimental studies would have to include tests of varying degrees of re-entrance and their effect on the evolving curvature, and the introduction of additional edge constraints that would endow the material with greater stability. Asymmetrically exerted forces on the pressure bars could also alter the negotiation of the one-dimensional auxetic properties along the panel’s path of bending. The eccentric bending apparent in Ill. 60 could therefore be derived from slight inaccuracies within the orthogonal positioning of the pressure bars that result in areas of higher and lower curvature.

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Ill. 60 Bending performance of the honeycomb

Analysis of the deformation diagrams The two diagrams show the compression (Ill. 61) and strain course (Ill. 62) of the material in four different individual stages. The analysis sheets indicate the employed auxetic cell, load case and maximum deformation values between unstressed or strained material and a neutral state.

In the stress diagram one can observe the bending performance of the material that immediately becomes apparent and amplifies when compression is increased, producing maximum curvature in the centre area of the panel that contains the most re-entrant cells. The material shows longitudinal elongation in the centre zones and shortening in the lateral edges. This behaviour is derived from the bending force that affects the re-entrant ligaments, which strain to unfold outwards. The surplus of material created in this fashion reverses the planned effect of purely longitudinal planar extension, according to which the specimen’s thickness should decrease. The effect differs from materials with a constantly positive Poisson ratio in the sense that the degree of elongation expands over time as a function of the pressure applied, geometry and material properties. Curvature control over panels shaped in this way can be achieved by calibrating these properties. A future study could attempt to design larger-sized panels in which zones of maximum and minimum re-entrance vary gradually to potentially facilitate more complex bending behaviour that could be architecturally exploited. In the course of the test the specimen’s width remained largely constant. For the retrieval of this measurement the highest point of the emerging arch was pushed down onto the testing bed. No thickening of the lateral edge areas was detected.

In the strain diagram a maximum longitudinal extension of 2.3 cm was achieved. The material showed high resistance to the strain forces applied due to structure modelled in accordance with the fabrication constraints. With a given cell size of ca. 0.75cm x 1.15cm, the proportional amount of material occupied 34% of the overall volume. In the future, altering the ratio towards diminishing amounts of structural material will lend the material greater reactivity, as the bulk density of the elastic material is reduced and thus poses less resistance to strain forces. In the 143

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measurement conducted here greater elongation of the cells was observed, of course, in the vicinity of the points at which force was applied. The envisioned local variation in longitudinal extension could not be recorded under the given force. On the other hand, an increase in the strain forces applied that would eventually release full unfolding could potentially endanger the integrity of the structure. As seen above, the aspect of scale is crucial to achieve the desired performance. Future research has to negotiate the material’s robustness with its degree of reactivity and the applied force needed to trigger the behaviour desired to fulfil the design goal. This aspect affects the general composition of additively fabricated building elements in two ways: a.

Thinner and more reactive auxetic structures require additional stiffer elements to contribute to the main load-bearing functions. The main structural element—besides the additively fabricated honeycomb—then has to compensate all load cases of the composite and provide resistance against such effects as torsion and bending forces. Such devised elements could be activated by smaller strain forces that would release the form-changing behaviour.

b. Thicker and more robust additively fabricated structures can compensate the structural loads acting upon the component more evenly, since the honeycomb panel itself is able to distribute occurring forces. A secondary, more lightweight element could provide the outer layer of additively fabricated elements and absorb the remaining forces. The activation of this inscribed performative behaviour would then require a higher strain force to unfold the re-entrant cells.

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Ill. 61 1D auxetic cell, load case: stress 145

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Ill. 62 1D auxetic cell, load case: strain 146

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5.1.2 Two dimensionally graded auxetics The second experiment will investigate a physical sample with bi-directional auxetic properties that integrates research by Roderick Lakes to design the auxetic cellular element (R. Lakes 1991). For an easier comparison between the 1D and 2D auxetic experiments, the sample is comprised of a bow-tie shape developed by Lakes, which also served as the basis for the principal design of the 1D structure with graded zero Poisson ratios. Analogous to the previous experiment, which developed a gradual distribution of longitudinal expansion through an alteration of the re-entry properties of the ligament, computer-aided design tools can be employed to control such geometries (Ill. 63). The experiment looks at the fabrication of a graded auxetic honeycomb in the dimensions 15 cm x 39 cm that contains cellular elements in the dimensions 0.8 cm x 0.8 cm x 3 cm (Ill. 64). The cellular geometry is defined as an auxetic bow-tie structure (see 4.1.3 Two-dimensional auxetic structures) with changeable degrees of re-entrance, resulting in corresponding degrees of lateral expansion.

Ill. 63 Geometric control of re-entrant cellular behaviour with an array of bow-tie-shaped elements

Envisioned experimental outcome The experiment investigates structures that can have an encoded and controllable bilateral extension when subjected to longitudinal strain forces. These structures show a gradual form-changing potential in two dimensions, which could be eventually exploited for larger building elements on an architectural scale. As stated previously, this formchanging potential can be triggered through a complexity of a bespoke material composition, illustrating the advantageous possibilities generically embedded in additive fabrication technologies. Each ligament is deformed according to a pre-defined set of parameters that ensures the ligament’s graded degree of re-entrance.

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Ill. 64 Top: topological design of the cellular element, bottom: geometric setup of the test specimen

Future research can be performed on a more irregular distribution of the cells’ re-entry characteristics. These can then be potentially exploited to create buckling performance as mentioned by Alderson (1999, 385) through stress scenarios that can be caused by laterally constraining cellular areas with high-entry ligament cells. The longitudinal extension could be constrained in the edge areas to shift the centre area of the panel upward (Ill. 65).

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Ill. 65 Lateral bending behaviour of 2D auxetic panels through edge unilateral vertical constraints

Known limitations As mentioned in the first example, the different re-entrant values must be assigned to the cells not arbitrarily, but with great care. Encircled islands of cells with high ligament re-entry values, surrounded by cells whose ligaments have low re-entry values, will be constrained in their ability to unfold their internal ligaments completely and thus exhibit increasingly positive Poisson ratios the longer they are subjected to stress. The experiments therefore use a linear gradient distribution of transformation values to provide for controlled unfolding (Ill. 66). All of the additive fabrication materials employed become brittle over time through exposure to daylight. This aspect requires the mechanical tests to be carried out with care to avoid damaging the sensitive material specimens.

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Ill. 66 Graded distribution of bi-axial auxetic behaviour

Scaling aspects of material performance must also be taken into account to study the transferability of the results.

Since additive fabrication requires a minimum thickness of the ligaments, a sturdy width of 2 mm for the cellular walls has to be defined so that the overall size is able to withstand the lateral forces applied. The minimum thickness does not have to be scaled up in larger-sized panels, providing for better reactivity to the stress or strain scenarios affecting the material. Physical prototyping and model analysis of these materials is necessary for the construction and design of larger-scale elements in the future.

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Testing of the samples The sample sheet documents longitudinal strain and stress forces as described in the previous experiment. During the stretching process the cells should unfold their individual degrees of re-entrant ligaments and allow a lateral growth to emerge. In the compression process the ligaments re-enter the cell geometry and lead to a partial thinning of the sample, especially in the centre areas where the specimen shows the greatest indentation. The cells’ behaviour should gradually shift from a positive Poisson ratio in both lateral seams and from zero to negative values in the centre of the panel. The experiment will measure the lateral expansion in the centre zone and on the edges. The experiments are documented by images to analyse the local unfolding of the individual regions, and to monitor the described switch from a negative Poisson ratio close to zero towards a positive Poisson value due to the different degrees of folding by the ligaments. The experiments should prove that a gradually varying distribution of Poisson values can be obtained by encoding the cells’ behaviour and temporarily applying lateral strain force.

Fabrication The prints are fabricated with a Connex 500 printer by Objet geometries Inc. equipped with the Digital Material TangoBlack with elastic properties. The build direction of the sample is perpendicular in the z-direction to the cellular orientation of the x and y-axes described above.

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Ill. 67 Connex print of 2D graded auxetic knot structure

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Analysis of stress and strain behaviour General performance The tested specimen showed mechanical behaviour under compression (Ill. 68) significantly different from that of the 1D auxetic cell tested above. The specimens were compressed by 4.8 cm in the longitudinal direction and showed less tear resistance. This property is probably based on the different geometry of the cellular element, which has varying degrees of folded longitudinal ligaments. Under increasing pressure the re-entrant property of the 2D auxetic cell revealed a considerable degree of re-entrance (Ill. 69) that could be tracked best in the centre zones of the bending panel. Normal deformation under applied stress created an arch-like structure as did the previous material, but revealed an obvious crease in locations of high cellular re-entrance. These zones distributed the forces irregularly over the entire structure to create structural cusps with uneven curvature flow. Once these areas were pressed downward an S-like form emerged, based on the forces acting on the re-entrant cells. Ill. 66 (left) shows the negotiation of occurring stress forces and the different degrees of re-entrance.

Ill. 68 2D auxetic structure—left: unstressed, right: stressed

Through vertical compression an additional structural constraint was introduced that increased the load, thus affecting the specimen by amplifying the auxetic effect of the individual cell. The similarity of 1D and 2D auxetic specimens allows differentiation of the two effects and showed that the auxetic cellular composition is responsible 153

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for the change in form. The bending performance is less traceable in the areas of subtle re-entrance and increases significantly towards the centre zones.

Ill. 69 Re-entrant cellular behaviour under compression load—left: flat, right: unflattened

A material specimen with a periodic distribution of an identical cellular element would create a regular, arch-like structure without lateral deflection. The 1D auxetic honeycomb introduced a longitudinal bending figure since the re-entrant cellular elements protruded outwards, releasing additional material that could be unfolded under compression. In the 2D auxetic material even more longitudinal deformations could be tracked, resolving in a curvature flow with two inflection points. Similar to the previous tests, the cellular scale and the required minimum fabrication dimensions affect the behaviour of the structure. The envisioned lateral expansion, initially conceptualised as the desired performance of the panel, could therefore not be achieved since the rigidity of the material prevented the ligaments from folding. To achieve such a behaviour the relationship between material and performance space would have to be changed in the sense that the material width of the ligaments would have to be reduced or the cellular sizing increased significantly.

The performance under strain forces resembled the behaviour of the 1D auxetic specimen and produced a gradual elongation in reaction to the stress force applied. The effect of the pulling force was dominated by the structural rigidity of the material and less by the geometry of the individual cellular morphology. The experimental results that can be extracted from the last two experiments favour the application of 1D and 2D auxetic structures for the creation of curved panels.

Future research could provide further knowledge on the relationship between cellular distribution and threedimensional forms. 2D auxetic honeycombs negotiate their cellular geometry and produce counter-intuitive morphologies that appear promising and require further study. The constraining effect of neutral auxetic cells can potentially trigger an irregular deformation in reaction to the compression applied. Since the deformation is controlled by two-dimensional numerical matrices, circular gradients (Ill. 70) can be encoded that could add further detail to the curvature flow along the edges.

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Ill. 70 Circular gradients of re-entrant behaviour expressed in a two-dimensional matrix

Controlled longitudinal auxetic performance appears achievable solely through larger cellular sizes and will become feasible once fabrication scales increase.

Analysis of the deformation diagrams In the stress diagram gradual deformation could be detected in three steps until a maximum compression of the overall length by 4.8cm was reached. The curvilinear edge flow became more visible when more force was applied to the lateral edges of the specimen. In the areas of low re-entrance the curvature radius was high, but became increasingly smaller towards the centre zone, producing two inflection points. The strain forces applied to the centre zones bent the re-entrant ligaments outwards in a circular fashion until the point of inflection was reached. Looking at the curvature flow one can thus deduce a correlation between the bending curvature radius and degree of reentrance. In larger-sized cells that yield a smaller θ angle smaller radii could be triggered, resulting in a higher number of inflection points. Curvature control of the longitudinal edge seams would have to utilise these parameters as design drivers for freeform panel deformation. Future research can study this behaviour with larger cellular sizing and circular gradients of high and low re-entrant cells. The computational model developed here allows a facile distribution of re-entrant values and calibration of the ligaments width to be adapted to future fabrication conditions.

The design drivers employed to define such two-dimensionally shaped auxetic honeycomb structures in arbitrary sizes and forms consist of spreadsheet information, a spatial U and V grid and a general calibration of the minimum and maximum states of re-entrance on a cellular level.

In the strain diagram a maximum longitudinal extension of 1.5 cm was achieved. The material showed a high tear resistance fuelled by its dense distribution of auxetic cells. The elongation process decreased slowly towards the fixed edge but did not correspond to the respective cellular properties. For a full unfolding of the cells a higher strain force 155

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was required to overrule the initial mechanical characteristics and activate the cellular unfolding. Lateral extension remained largely constant and did not show cell-specific performance. Compared to the previous 1D auxetic test, the dimensionality of the specimen chosen here appears better suited for compression load cases and their performative behaviour, whereas the structural stability of the additive fabrication material and the high amount of strain required are less encouraging. In order to avoid deterioration of the material, a broader impact area has to be devised that clamps the lateral part of the structure and fixes some of the re-entrant cells into position, thus affecting auxetic performance in these areas. Build directions have to be chosen in accordance with the material’s desired performance. Once the primary force direction has been identified, the build direction must be placed orthogonal to the force vector to avoid a further weakening of the mechanical qualities.

The final two experiments stressed the importance of material scale in the modelling process and its impact on the reactivity of additively fabricated created structures. For a successful design the following workflow is suggested: 1. Identify the desired material performance 2. Identify the main force vectors 3. Define the contact zone 4. Dimension of the material composition in accordance with the desired performance 5. Identify the build direction 6. Fabricate It can be expected that a better reactivity of strain-induced auxetic structures can be expected with larger fabrication dimensions. Beside these foreseeable advances, over time the material qualities present an additional obstacle to integrating such materials as building components. Polyjet-printed parts with elastic qualities become brittle in a short time and lead to complete deterioration of the material. Future research must investigate composite structures that contain additively fabricated elements which then must be teamed with more robust protective and performative layers to ensure their full usability over longer periods of time.

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Ill. 71 2D auxetic cell, load case: stress

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Ill. 72 2D auxetic cell, load case: strain

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5.1.3 Three-dimensionally graded auxetics The design of materials with three dimensional auxetic performance is still relatively new and was first described in the late 1980s by Roderick Lakes (see previous chapter).58 To date, three-dimensional auxetic cellular structures made out of polymeric materials can only be manufactured mechanically through a process that was described by E. A. Friis (1988). The process involves compressing thermoplastic polymer foam along three axes until re-entrant buckling effects start to appear on the cellular ribs.

Friis et al. describe this process as follows: “For thermoplastic polymer foams, the procedure entails tri-axial compression by a factor of 1.4 to 4 in volume, followed by heating to a temperature above the softening point, followed by cooling under the volumetric constraint. For metallic foams made of ductile metal, the procedure consists of applying uniaxial compression at room temperature until the foam yields. Additional compressions are applied sequentially in each of three orthogonal directions until the desired volume change is achieved. The thermal transformation technique used on thermoplastic foams would, in principle, be applicable for metal foams.” in E. A. Friis (1988, 2) These foams show stronger stress resilience properties than conventional foams.59 “When an object hits an auxetic material and compresses it in one direction, the auxetic material also contracts laterally— material ‘flows’ into the vicinity of the impact. This creates an area of denser material, which is resistant to indentation.”

(Alderson 1999, 384) Besides these factors that influence the general properties and maintenance of materials, one can imagine that actively controlled form-changing behaviour in three dimensions can be developed that is triggered solely by applied stress and strain forces. Analogous to 1D and 2D auxetic behaviour, these materials would allow a dynamic performance to emerge that could be based solely on the specification of cellular re-entrant values and be released by devices that impose stress or strain forces on the respective material. This form-changing behaviour can be actively engaged as a design parameter and would allow the production of three-dimensionally deforming elements like single- or multiple-layered panels of volumetric cellular clusters. A precise control of the emerging morphology of the structure can be obtained with the aid of parametric modelling tools and additive fabrication devices, since the mechanical process that was presented by Friis and Lakes hinders accurate control over the individual paths and degrees of the re-entrant ligaments within the cells.60 Thus a closer look must be taken at the geometry of suitable individual cellular units and the geometric control options of such structures. In the above mentioned paper, Friis et al. presented an idealized cellular geometry of a re-entrant foam structure (Ill. 73) drawn from an analysis of the polymeric foam.

See here R. S. Lakes (1987).

The resilience of a strained body is hereby defined as the ability to recover its size and shape after deformation caused especially by compressive stress.

60 For single layered auxetic foam structures punctual deformations of polymeric foam materials though local stress control are imaginable, but a creation of multi-layered foam structures with differing internal re-entrant values cannot be achieved using the method Friis presented based on tri-axially applied planar compression forces.

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Ill. 73 Unit cell of re-entrant foam—illustration taken from E. A. Friis (1988, 7)

Parameterisation of a cellular unit based on E.A. Friis’ idealised knot In the course of the experimental investigation a digitally controllable model based on Friis’ idealised cellular unit was encoded by a CAD tool that allowed precise control over the translations of the various cellular hinges. To allow a stacking of the cells, the outward bending ligaments of the idealised cell were mirrored inwards, while maintaining the same surplus length needed for the auxetic performance to emerge. The unit cell, consisting of linear elements and hinges, was coded in such a manner that the end points of the lines operate in a relational constraint to the other member’s spatial position and receive dependent x, y and z-coordinate information driven by a binary matrix of numerical values corresponding to the lattice sub-divisions in the lateral and longitudinal directions. The control over the path of the hinge points allows practical management of the re-entrant properties of the individual ligaments.

The numerical values do not represent absolute spatial coordinate values, but define relationships that are scaled in the modelling progress to comply with the local boundary conditions. This aspect thus allows a general tuning of the auxetic properties in both the local and the global domain.

In contrast to the conventional manufacturing system proposed by Friis and Lakes, in this material each cell can be configured individually and assigned a specific auxetic characteristic. As previously stated, a gradual distribution of auxetic values is favourable since extreme neighbourhoods of differing re-entrant values can constrain the unfolding of the ligaments. A digital model of stacked cells (Ill. 74) was modelled (Ill. 10) with a gradual distribution of the reentrant values and printed with a Zcorp machine for visual testing (Ill. 75).

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Ill. 74 Parametrisation of Friis and Lakes’ auxetic knot element

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Ill. 75 Plaster-printed model of graded 3D auxetic knot structure

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Parameterisation of a unit cell based on R. Lakes’ idealised knot For the physical testing of the auxetic structure, a second knot was parameterised that was initially proposed by Lakes in his paper on foam structures with negative Poisson ratios of 1987 (R. S. Lakes 1987). The original knot geometry—again, produced by a multilateral compression of polymeric materials—consisted of cubical array of compressed 24-sided polyhedra joined by linear elements on each of the six sides. This type of stackable knot as a lattice cell was preferable to Friis and Lakes’ idealised knot because it guarantees a lateral expansion of the ligaments under longitudinal stress. In the case of orthogonally applied stress or strain towards the four-sided elements of the Friis/Lakes cellular module only a lateral expansion appeared imaginable and therefore critical. In the cellular element discussed below a trilateral expansion is guaranteed by the unfolding of the re-entrant ligaments that are controlled by the linear elements connecting each cellular unit.

Ill. 76 Idealised 3D auxetic cell from a symmetrical collapse of a 24-sided polyhedron with cubic symmetry (R. S. Lakes 1987)

This parameterised knot structure can be tuned in terms of the degree of the re-entry of the ligaments through relational control of the coordinate positions of each of the hinge-like end points (Ill. 77). This encoding allows the range of potential auxetic performance to be calibrated.

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Ill. 77 Encoding of the idealised unit by R. Lakes

Each of these hinge points behaves in coordination with the others and can populate a wide range of lattice structures. The connection of the spatial position is defined with topologically invariant properties that allow scaling to the desired component size. For a completion of the modelling process the linear elements have to be modelled as 164

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volumetric entities under the scale-dependent structural conditions. For the creation of watertight meshes the volumetric modeller Symvol for Rhino (Uformia AS 2011) was used, which allows a blending between the individual volumetric geometries.

Additive fabrication is very suitable for even highly complex structures that are populated by auxetic knots as demonstrated in the following illustration (Ill. 78) of a catenoid helicoid-based surface with a periodic distribution of auxetic cellular members.

Additive fabrication can easily reproduce such designs that are impossible to fabricate with conventional manufacturing processes.

Ill. 78 Catenoid-helicoid surface with a periodic tiling of maximum-re-entrant 3D auxetic knots

The proposed experiment constructs a single-layered array of three-dimensional auxetic knots with a gradient distribution of re-entrant values responsible for the expected Poisson ratio. The structure consists of a twodimensional array of 13 x 5 cells with each individual cell 30mm x30mm x 30mm in size. The overall dimensions of the test are 390 mm x 180 mm x 30 mm. The structure shows the maximum re-entry values in its centre and their gradual reduction towards the outer cells (Ill. 79).

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Ill. 79 Single row of auxetic cubic elements with gradual distribution of re-entrant values

The experiment is designed to deliver a structure that allows an analysis of the knots’ behaviour with regard to applied strain and the related form-changing effect. The behaviour is analogous to the 2D auxetics: based on coordinated performance between the ligaments’ geometry and the mechanical properties of the print material employed, complex mechanical performance can be triggered easily under stress and strain.

Ill. 80 Implementation of the specimen

Envisioned experimental outcome It is expected that the sample will show trilateral expansion in the centre zone occupied by the auxetic nodal cells with high re-entrant values. This expansion should gradually decrease towards the shorter lateral edges, indicating a shift from negative to positive Poisson ratios. The experiment will also investigate the form-changing potential of the 166

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enclosed and edge cells under various degrees of re-entry. The sample will be tested under stress and strain that would otherwise lead to opposite deformation performance. Strain should lead to expansion and stress deliver a trilateral thrust fault, bringing a tri-axial reduction of the bounding volume of the individual cells in the centre zone and trilateral expansion of the edge cells.

Known limitations The test sample will not take the anisotropic material properties present in additive fabrication processes into account for the definition of the tubular diameters. The investigation focuses on the general functionality of the parameterised nodal component and the elementary material performance. The experiment represents a first translation of a parameterised nodal element with the help of additive fabrication that has been taken from mechanically deformed polymer foams and offers a basis for future research on the transferability of findings across fabrication boundaries. The primary research target lies therefore not necessarily in an exact prediction of the structural behaviour of the individual cells, but rather in its monitoring the systematic deformation that should be readable under stress and strain forces. The experiment is designed to deliver a high reactivity of the structure by reducing the tubular diameters to the technologically acceptable minimum. Tube diameters of 2 mm and 3 mm for the connector pieces has been chosen to allow for a safe support structure removal process with pressurised water (Ill. 81).

Ill. 81 Printed model before removal of the support structure

These tube dimensions nevertheless create geometric intersections in the corners that can structurally constrain the flexibility of the knot. Since the relationship between cell size and tubular diameter is not directly dependent, this effect can be diminished for larger-sized panels to allow more reactivity by the individual cells. The best articulation of the auxetic performance can be achieved by thin tubular dimensions sized around 3-5 % of the maximum cell dimension. This sizing prevents a twinning of the ligaments in the corners of the cell. Thicker tube dimensions can lead to a stiffening of the corner areas and deliver a counterintuitive behaviour of the cell geometry.

To provide for safe support structure removal, intercellular tubular connections were modelled that were cut after the finalised print.

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Ill. 82 Graded distribution of tri-axial auxetic behaviour

Testing of the sample The sample will be tested under laterally applied stress and strain to monitor the envisioned gradual unfolding action with the already known devices. Since the layered array of additive fabrication produces different mechanical properties that affect the elongation-at-break61 values of the ligaments in the various spatial orientations, the stress and strain forces have to be applied carefully to prevent damage. The build direction of the structure has been devised in such a manner that there are no nodal components under tension with stress or strain parallel in any direction. Over the course of testing the structure is subjected to tension through a gradual increase of selected pressure until a maximum unfolding of all cells has been achieved. The experiment correlates the local extension in relation to the applied force flow in three dimensions and charts the evolving deformation that can be detected.

Fabrication The specimen is printed with a Connex 500 machine by Objet Inc. using the elastic digital material DM 9885 that contains a Shore A range of 85. The build direction of the sample is perpendicular in z-direction to the cellular orientation of the x and y-axes described above.

61 Elongation of break can be described as the “Tensile elongation corresponding to the point of rupture�. Testing methods and definition can be found in the ASTM D412 or ISO 37 standard procedures.

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Ill. 83 Connex print of 3D graded auxetic knot structure (red lines identify the temporary structures modelled for safe support structure removal) and cut after cleaning 169

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Analysis of stress and strain behaviour General performance The resulting 3D auxetic structure showed great longitudinal and lateral flexibility once the temporary connectors were removed. The movement potential was driven mainly by the four linear connections (diameter 3 mm) located in the centre of each lattice cell, which created a grid connecting the individual cells. The required material thickness of the remaining tubular elements was modelled with a diameter of 2 mm. This dimensioning led to higher material density in the cellular corners and constrained the performance potential. Under lateral compression this aspect became crucial since the individual cells reacted to the occurring stress not with a higher degree of re-entrance, but through an overall crushing of the cells. This effect can be seen in Ill. 84, where vertical stacking of the cells is visible.

Ill. 84 3D auxetic structure—left: unstressed, right: stressed

The morphology of the structure under compression would continuously develop new configurations of cellular stacking if the testing process were repeated. This aspect hindered reliable measurement of such behaviour. For this reason one exemplary configuration has been mapped, but other comparable values are imaginable. A further compression of the structure beyond the point presented here was rejected since individual tubes were experiencing torsion and shear forces that appeared potentially harmful for the structural integrity of the specimen.

The performance of the specimen under strain forces showed high linear elasticity and elongation values, but no lateral expansion. It appeared that the main part of the longitudinal elongation was based on the general elasticity of the material and only a limited share due to the unfolding of the re-entrant cells. Nevertheless the latter could be observed in the centre parts of the specimen, where highly re-entrant cells where located.

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The fabricated structure exhibited spatial adaptivity to an altered morphology of the base surface and even allowed double curvature flows (Ill. 85) since local elongations of the connector elements were observable, teamed with the unfolding of the auxetic cells. The illustration shows the deformation behaviour of the material sample when placed on a cylindrical element. Gradual variations in the cellular gaps provide a smooth structural flow and potential adaptivity to a wide range of base shapes.

Ill. 85 3D auxetic structure with gradual degrees of lateral expansion; red arrows indicate strain forces acting on the central knots This aspect promotes applications of such material in composite structures used for curved panels, in which the 3D auxetics could operate as spacer material that adapts to a given geometry. The shock-absorbing properties of auxetic material under vertical impact could be adjusted to varying degrees of re-entrance in the most critical zones within the panel. Once the dimensional relationship between minimal material thickness and cellular sizing has been altered, these properties could be coupled with a stronger articulation of the inherent form-changing potential of the auxetic cellular elements, since a stronger reactivity could be expected. In the example presented here a further unfolding of the centre zone could be imaginable under these altered boundary conditions.

The experiment conducted here underlined once more the relationship between material scale and performative domain. Looking at all of the tested examples, the remaining issues with regard to fabrication sizes and the mechanical properties of the employed materials still pose an obstacle to the full integration of additively fabricated structures in building scale. While the first aspect appears to be solvable over time, the second, especially for materials with low bulk density, is a critical aspect that requires further developments in material research. Material deterioration over time and weak resistance against point loads require elaborate preventative measures that interfere with the envisioned simplification of dynamic building components at the root of this research. Nevertheless, the tests performed here show that the computational tools developed to define such structures do work and deliver a controllable interface with great openness and adaptivity. These developed tools can then be integrated and adjusted 171

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to upcoming fabrication developments and guide a more straightforward behaviour of dynamic auxetic morphologies.

Analysis of the deformation diagrams As stated before, the deformation diagram of the specimen under compression represents only a momentary state of the structure’s behaviour. Over the course of the test the structure was compressed by 2.8 cm and showed irregular cell stacking in the middle part of the specimen, mixing the elastic properties of the print material with the limited reentrant performance of the cells. Further compression of the material appeared possible but could have affected the structural stability of individual cellular geometries since eccentric forces could potentially shear the cellular tubes at their position in mid-field.

The geometric blending of the knot’s corner areas, where six individual tubes intersect and connect in a single point, defined zones with higher stiffness that operated as distributed load planes, preventing the transfer of the stresses to the individual ligaments and limiting their freedom of movement. The envisioned auxetic behaviour that guided the design was therefore not observable as such in all three dimensions.

Under strain forces the material achieved an elongation of 6.6 cm, the highest of all experiments. The individual elongation lengths grew depending on the location of the applied force, promoting the perspective that this deformation is based predominantly on the elastic material properties of the fabrication material and less on the degree of re-entrance. It appeared that the stiffening of all eight corners produced elastic, but more rigid cells that would prevent an unfolding of the ligament’s geometry even under a strain force exerted by the connector pieces placed mid-way along each of the four sides of the cell. The envisioned trilateral expansion could therefore not be achieved since no triggering of the unfolding of the tubes through the applied forces could be observed.

The connection between each cell row was achieved by two lateral and two longitudinal tubular geometries with a diameter of 3 mm each that coupled the complementary points at mid-span of the neighbouring cell. These connections are most stable when the applied forces act parallel to the course of the connector geometry. Eccentric loads produce momentum forces on the flexible support at mid-span and can lead to critical mechanical behaviour.

Since the structure is highly flexible as it is connected to only a limited number of intercellular connections, these points become vulnerable when handled without care. Taking the above into consideration, one can conclude the following: An application of 3D auxetic cells for functioning building components and controlled change in form is still not fully feasible under the given technological boundary conditions. Existing geometric and material constraints affect the reactivity and stability of additively fabricated material specimens. An investigation of auxetic cellular structures as internal composite material for freeform panels appears advantageous since an adaptivity of the structure to arbitrary shapes can be attempted. Research should take advantage of the shock-absorbing properties of such materials and calibrate cellular geometries depending on the expected load case to potentially deliver lightweight and more robust panel materials in the future.

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Ill. 86 3D auxetic cell, load case: stress 173

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Ill. 87-1D auxetic cell, load case: strain 174

Emerging Architectural Potentials of Tunable Materiality through Additive Fabrication Technologies

5.1.4 Conclusion The conducted experiments proved that additively fabricated materials can be employed to create mechanical changes in form driven by auxetic cellular components in one, two and three dimensions. The tests operated with a singular materiality that was aligned to the digital geometries of parameterised cells. The tuned structural behaviour depended on the macro-scalar structure that was combined with the properties of the single polymeric material given by the employed additive fabrication technology. The following experiment approaches tuneable mechanical behaviour through a combination of molecularly differentiated polymers that are then applied to a periodic macroscalar geometry.

The individual sub-conclusions have outlined the existing limitations that affect the mechanical sensitivity of the specimens towards the desired form-changing behaviour. The research has proved that novel possibilities for architectural applications are imaginable since individual mechanical performances can be integrated into the structure. These properties can affect inscribed form-changing potentials or gradual flexibility that is achieved locally through control of the material’s structural composition. The allocation of performative complexity through tuned material morphologies was shown in principle, encouraging the performance of future studies. Remaining constraints for building applications can be found in the high costs required for the production of such materials and insufficient knowledge about their long-term performance in the build environment. Additively fabricated components in larger sizes that could be employed for such components as façade panels with dynamic form-changing potential require a manufacturing process geared towards the building sector as far as the material properties and necessary tolerances are concerned. The development of fabrication technology with polymeric materials for such applications has not been approached by industry yet and is probably decades away.

The experiment further proved the viability of the methodological approach that beneficially integrated research knowledge from the field of material science by transferring of the geometric dependencies that are described in the individually parameterized auxetic cells. The topological codification of these cellular components allows their readaptation to future fabrication developments that expand the potential material properties and achievable build sizes. The relatively facile alteration of intercellular dependencies paves the way for further research on cellular elements with innovative performative profiles. These can be coupled with local dimension control of the easily controlled ligaments of the individual knots. A demonstration of combined cellular alteration and ligament dimensioning can be found in section 5.3.2 Weaving.

The role of the experiments described in the methodological chapter addressed this desired transferability of the experimental results. The definitions and dimensions of the individual cellular entities nevertheless have to be brought up to scale for the later components and aspects integrated like self-weight, buckling behaviour and other conditions vital for the materials’ structural stability and performance profile.

The properties of additive manufacturing and recent digital design tools have been employed successfully to construct a material with high amounts of local geometric variation that cannot be achieved with classical fabrication procedures. Especially three-dimensionally auxetic knots with continuously varying spatial extensions underline this advantage of additive fabrication over other manufacturing methods.

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Experiment II: Heterogeneous Material

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5.2.0 Introduction The first two experiments investigate computational and fabrication workflows to calibrate graded mechanical properties of additively manufactured materials. Whereas the first experiment develops a method for the control of such properties by adjusting a single material’s structural morphology, the experiment conducted here investigates the regulation of graded structural behaviour through the combination of different materials with distinct mechanical properties (Ill. 88).

It can be argued that this semantic differentiation is only partly correct since the structural effects also govern internal material composition on the micro-scalar level of the multi-material composite experiment that will follow here. The quality and definition of the molecular bonding structure in a linear, cross-linked geometric or electrochemical arrangement produces significantly different material properties.

It goes without saying that a combination of these two methods is feasible, but this goes beyond the scope of this thesis. It is the author’s belief that the complexity observable in the behaviour of such materials requires a sequential research process that develops a prior understanding of the individual performance achieved within the two described fields before it can proceed to the more complex combination of both.

Ill. 88 Left: material differentiation, right: structural differentiation

The fabricated materials show local performance properties rendered by the momentary boundaries of developing computational and fabrication technologies. The interconnection between the digital process and its materialisation can lead to a future expansion of the scope, scale and accuracy of material performance created in this way. The ability to exert modest control in three dimensions of the material’s morphology and mechanical properties even today nevertheless encourages contemplation of its architectural applications. One of the key aspects in this context is the ability to allocate a different locus where performative aspects are integrated in the material. The calibration of material performativity through the definition of a bespoke internal structure and/or material composition embeds the complexity in a material tectonics that is variant and locally defined. The experiment, although modest in its functionality, illustrates this potential clearly, since traditional methods to achieve comparable performance are usually bound up with assemblies of multiple components and elaborated methods of mechanical and intelligent movement control in an orchestrated assembly sequence.

A practical architectural application of such a process could lie in replacing separate mechanical devices that allow building components to move, like hinges, in favour of material alteration of its local substructure to allow a seamless integration of surfaces with varying inscribed subcutaneous functionalities. Further studies could be conducted on the application of materials that interact with the user’s behaviour in a structural manner, providing elasticity and stability where needed.

The samples and workflows presented here serve as a preliminary demonstration of the intensive properties of such a new material and point to the distinct advantages of the fabrication process for its manufacture. These processes are developed in accordance with the currently available fabrication parameters and require adaptation to changing

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scales to ensure structurally sound performance. These aspects open up another research field for the future that focuses on these correlations between structural and material composition as they relate to fabrication scales.

5.2.1 Experimental goal The experiment creates a three-dimensional, mechanical heterogeneity of local stiffness values through material differentiation while maintaining periodic geometric composition. The experiment builds upon recently developed multi-material additive fabrication technology that allows a three-dimensional distribution of mechanically differentiated cells. Bhashyam, Shin and Debashish’s proposed “variant approach” for the calibration of heterogeneous materials will provide the structure upon which the computational design process is built. This design method will employ structural analysis software as a design driver to create a 3D heterogeneous performance profile from which the internal material distribution can be deduced and deliver gradual distribution of the mechanical properties within the test specimen. In the following the additively fabricated physical specimen will be checked mechanically and visually for correlation with the envisioned digital performance profile.

With the arrival of more differentiated printing options and materials (especially metals) the design methodology could be tested for the specification of alternative graded properties and more complex cellular and matrix geometries. The envisioned ability to control dynamic, mechanical, electrical or other material properties through the geometric and material construction of an additional third build axis allows for an expanded specification of the components’ functionality. The test therefore has to be viewed as a proof-of-concept for a locally defined graded materiality that is created by layered manufacturing under the existing constraints of today’s fabrication technology. The text will specify the limitations of the process due to fabrication and geometric issues.

5.2.2 Boundary conditions of the experiment The experiment requires four parameters to be examined and their boundary conditions investigated. Once the chosen method for each of the respective categories has been identified, the model can be assembled, computationally translated into a suitable three-dimensional geometry, meshed, printed and tested. Each parameter must be devised in concert with the other relevant parameters and aligned with the specific constraints associated with them, e.g. the tectonic parameter that identifies the way material is arranged three-dimensionally must comply with the production parameters defining scale and file sizes to allow proper manufacturing of the test piece.

Tectonic parameters The chosen method for the tectonic parameters picks up on the principles described in the review of literature on the production of two-dimensionally graded materials and alter the tectonics into a third dimension of material heterogeneity under the aspects of additive fabrication.

Material specification parameters A method is developed that distributes material in accordance with an approximation of goal-based mechanical behaviour. This process implements findings from existing research on functionally graded material and transfers them to additive fabrication. The research describes a computational method for a three-dimensional distribution of 178

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material with changing degrees of elasticity within a test sample, adapting the variant approach by Bhashyam, Shin and Debashish.

Production parameters The production parameters describe a method for the additive materialisation of such materials with the help of recent multi-material technology by Objet Geometries Inc. and outline constraints that still apply to the material qualities and scope of mechanical properties that can be implemented in their production.

Analysis parameters The last part outlines the mechanical and optical testing methods. The created sample is subjected to magnetic resonance technology (MRT) and mechanical testing according to DIN EN ISO 604.

5.2.3 Tectonic parameters Functionally graded materials62 exhibit a migration of mechanical properties within a building component through a laser-induced process that melts differing ratios of two source materials. In this process a gradual molecular alteration within the material zones is achieved, due not to individual mechanically differentiated building blocks but the blending of the materials in the manufacturing process itself. Contemporary additive fabrication processes, on the other hand, can only provide pre-mixed sets of up to 14 materials in a single build that have to be geometrically assigned to individual, space-filling volumetric entities. Modelling software for heterogeneous solids allows the specification of volumetric geometries with a gradual distribution of internal material properties,63 yet fabrication of such is still not achievable. This constraint requires material distribution to be controlled through a periodic distribution of geometric “containers� in three dimensions, which are assigned their mechanical properties locally so that they achieve heterogeneity through composite interaction. This approach is visualised in an explanatory diagram (Ill. 89) for a process by Holmes and Mc Kechnie (2001) that can serve as an analogy for a computational process for modelling polymeric material composites in three dimensions. In the diagram the gradual transition between copper (20) and nickel (10) is achieved through individual blending ratios (30) of both materials.

See 4.2.3 Functionally Graded Materials (FGM).

See among others Jiao, Stillinger and Torquato (2008), Bhatt and Warkhedkar (2009), Jackson et al. (1999), Liu et al. (2003) Cho et al. (2005).

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Ill. 89 Left: material distribution diagram right: combustion chamber coating by (Holmes and Mc Kechnie 2001, 2)

The potential to expand a two-dimensional gradient known from the classical FGM process by adding a third build axis of gradual materiality appears promising. Yet the possibilities for robust materialisation are still limited and can only be achieved with the mentioned Connex (Sagi 2007) technology. The mechanical qualities of these digitally created materials are weak due to the fabrication process that delivers anisotropic mechanical properties dependent on the direction of fabrication. Future research into the development of fabrication processes with stronger mechanical properties and non-polymeric materials like graded metallic alloys is therefore needed.

In order to additively fabricate a material with varying properties the design of the individual building blocks that support the different build materials is important. These individual space-filling cellular elements should be devised in such a manner that geometry-based peak loads due to non-orthogonal loading or specific cellular geometries should be avoided. In a preliminary test to study an appropriate shape of such spatial elements, octahedral and cubical elements (Ill. 90) showed local peaks that would occur in specific areas of the element and cause bending forces in the neighbouring cells (Ill. 91).

Ill. 90 Material composite with truncated octahedral and cubical elements

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These peaks bound up with the specific geometry of the building block could only be evaded through a spherical geometry that would allow a smooth translation of the stress occurring along the curved surface. Since a test sample composed solely of a three-dimensional array of spheres would minimise the physical contacts to six nodes per sphere, an alternative solution had to be devised. The research performed by Hiller and Lipson (2009) that used spherical elements and encompassing matrix material was chosen as a feasible approach for the process conducted here. Accordingly the first material serves as a matrix in which the geometrical entities containing the five print materials are embedded. This approach minimises the amount of print materials that can be calibrated from six to five, since one material is reserved for the matrix.

Ill. 91 Left: material distribution within matrix material, right: peak loads in cubical geometry The distance between the individual spheres within the matrix can be calibrated in such a manner that delayed unfolding of the mechanical performance appears achievable. Under a vertical load the matrix material would first be compressed until the compressive forces are translated to the individually defined spheres. This effect should be observable in the later mechanical test, as the performance during the start phase is altered when the matrix material is compressed. The relationship between the spherical geometry and the encompassing matrix would allow the mechanical behaviour to be scaled, releasing either a stronger reactivity of its inscribed mechanical properties through a smaller zone between neighbouring spheres, or a weaker effect in which the matrix material adopts the overall mechanical performance, only slightly affected by smaller spherical geometries.

5.2.4 Definition the material specification method In a next step a computational process has to be devised that allows mechanical properties to be assigned to the discrete building blocks that have to be made to correspond with the digital materials. This is conducted with the help of finite element analysis, used as a design driver for the material selection. As stated in the literature review, digital processes for creating graded mechanical performance can be differentiated into generative and variant approaches, both of which utilise this analysis method for the material specification.

A classical generative approach can be found in topology optimisation processes that allow the definition of load-bearing structures with optimised material distribution by identifying the structural boundary conditions like forces, material properties, voids and bearings to an abstracted design space. This sub-divides the virtual design space into discrete mesh elements that compose the volume on which the iterative differential calculus of the structural scenario is conducted. The accuracy of models created in this way depends on: 181

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a.

the sub-division ratio of the virtual design space

b.

the calculus iterations conducted on the model

The examples shown below () explain the main workflow for the creation of such optimised structures. The definition of the loads, constraints, bearing and voids has to be assigned to a design space. In a next step a sub-division ratio of this volume has to be applied, in our case expressed by the line grid visible in the sectional diagram. In the last step the iterative calculation is conducted on each individual building block to define the presence or absence of material. In the three test cases presented complex morphologies emerge that negotiate the given structural and spatial boundary conditions. A re-meshing of this created geometry underlines the organic material distribution that can emerge from such a process. The irregularity of forms, including undercuts and branching, challenge classical manufacturing methods within an architectural context but might find application in mega-scale additive fabrication once the technology can provide for sufficient material properties.64 The sub-division ratio of the design space is intentionally reduced in this example to demonstrate the idea of sub-divided design space. In the example presented here a binary differentiation between material and non-material has been calculated, yet Hiller and Lipson’s research on the multi-material topological optimissation of structures and mechanisms of 2009 has already provided a workflow that integrates gradual translation between three differing material properties within the design space for Connex materials.

Ill. 92 Topology optimisation of constrained force flow within abstracted design space

Advances in CPU speed and CAM manufacturing have started to promote an application within architecture. The creation of such structures is based mainly on subtractive manufacturing processes. See here Sasaki (2007), Dombernovsky and Sondergaard (2009), Xie et al. (2011) and Burry et al. (2005).

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Topology optimisation constitutes an interesting research field for the development of load-bearing structures that are optimised in terms of material, and can potentially be fabricated with large-scale additive fabrication methods like the above-mentioned Dshape process (Dini 2010). Future research can further couple these geometries with space-filling microstructures that can dissolve the solid material into individual nodal elements and tune their morphology to the stress or strain scenarios they experience by adjusting their cellular sizing or the local dimensions of their individual nodal elements, to allow powerful, lightweight structural systems with minimal material consumption. This vision of additively fabricated micro or macro-structures still requires significant progress in the field of computational modelling and simulation to allow feasible file sizes and design development in reasonable timeframes. Interesting emerging research on the mesh-free modelling of micro-structures has been performed by e.g. Fryazinov et al. (2011).

Variant approach The proposed test sample develops a desired performance profile using a finite element method. In the physical sample three graded zones with varying elasticity should be created that are approximated by six polymeric materials from the Connex range. Certain structural limitations of these materials can be observed that will be further explained in the description of the production method. The sample combines the different mechanical properties of the available material selection as a multi-material composite through a sorting algorithm that correlates vertical deformation ratios to a selection of material.

The assignment of materials to create graded elasticity follows the processoral steps described in the variant approach for implementing the digital model.65 The workflow proposed here was developed by Bhashyam, Shin and Debashish for the performance-based solid modelling of fully heterogeneous materials and has to be adapted to the boundary conditions of additive fabrication where necessary. In contrast to the generative approach, which allows only limited pre-conception of the evolving artefact, the variant approach starts with a user-defined initial source geometry that is then calibrated in its internal mechanical composition. Table 1 gives a first outline of the steps conducted, but further information on the content of the individual topics will be provided in the following paragraphs.

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Table 1 Material specifications

Definition of the test volume and specification of the FE model The experiment sets up a Finite Element (FE) model66 from eight-node-hexahedral elements in a resolution of 50 (width) x 50 (length) x 12 (height) cells. These hexahedra elements that circumscribe a box-like volumetric space are chosen for their correspondence with the later cellular building blocks that contain the spheres and the encompassing matrix. The entire digital analysis block is composed of 30,000 individual cells. The chosen sample size of 100 mm x 100 mm x 24 mm corresponds to a suitable format for the mechanical testing procedures described later.

The meshed digital volume is assigned a homogenous materiality that mimics the Connex Vero White Full Cure 830 material properties67 with stiff mechanical behaviour. Since the company provides only a limited specification of their digital material’s mechanical properties, an ABS plastic material from the software’s library was selected as an approximation.

In a next step the constraints and forces required for the analysis were allocated. The four vertical sides of the block were restrained mechanically and three vertical forces (Fa=-600 N, Fb=-400 N, Fc=-300 N) were positioned on the top. The elasticity of the final material should reveal local peaks in the material’s elasticity in the areas where these forces were applied. The experiment creates two additional specimens with varying force values68 that will also be printed and tested. An analysis of these retrieved values will be given later in the text. The forces were confined to a circular area of 10 mm diameter each (Ill. 93) corresponding to the spatial position of the stamp used in the later mechanical test of the fabricated sample

FE software “ALGOR simulation professional” (Autodesk 2010) Elasticity module: 2.7579e+12 mPA, Poisson ratio: 0.36, shear modulus of elasticity: (N/cm^2): 101390 68 Test block 2: Fa=-400 N, Fb=-300 N, Fc=-150 N; Test block 3: Fa=-200 N, Fb=-150 N, Fc=-100 N 184 66

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Ill. 93 Implementation of the FE model

After the FE analysis the vertical deformation values of the hexahedral nodes could be extracted (Ill. 95). Each value is coupled with the spatial position encoded with coordinate information. From these local deformation values specific E-modules (modulus of elasticity) would have to be assigned from which the specification of the later print material could be derived. Modulus of elasticity is defined as a combination of stress and strain values and gives an indication of the material’s deformation properties. Here stress is the ratio between load and area, while strain is described by the difference between initial length and deformation length of a test object. Since the analysis provides the deformation length in the vertical axis, the strain value can be extracted (Ill. 94) from this and site-specific relational moduli of elasticity calibrated between the individual cellular elements. As the FE method delivers the coordinate and the displacement information, together a specifically layered point cloud can then be modelled in which the geometric position and the resulting values could be combined. The recorded deformation values extracted from the FE model can be sorted in such a manner that higher deformation values would lead to an assignment of more flexible print material, whereas lower deformation values would correspond to a harder print material.

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Ill. 94 Extraction of vertical displacement information for definition of composition control

To correlate these values with a potential print material, the overall numeric domain was sorted into five individual sub-groups that corresponded to the available print materials from Connex. In the digital model each sub-domain of points was separated into a single layer corresponding to a designated Connex material. This array of sorted points with individually described x, y and z-coordinates can then be attached to the spherical geometry with the desired radius and the correct material (Ill. 95). This point cloud with attached spheres is then embedded in a matrix material of higher flexibility to allow the fabrication of a functional test piece. Each cellular block with the dimensions of 2 mm x 2 mm x 2 mm therefore houses a single sphere with a radius of 0.9 mm.

Ill. 95 FE-based material distribution

The experiment applies this method to three differently structured blocks of equal dimensions and employs the same selection of materials for the spherical and matrix material. The three test objects should show different ratios of elasticity that correspond in their individual relations to the stress forces applied to the individual FE model. Since 186

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each calculation process retrieves a different set of vertical deformation values, a characteristic range of material distribution should be observable in the design specimens.

5.2.5 Defining the manufacturing parameters The research produces physical prototypes with an additive fabrication technology that was introduced to the market

by Objet Geometries in 2007. The technology allows the simultaneous printing of up to 14 photo-polymeric materials with differing physical properties that affect stiffness or translucency (Sagi 2007). At the time of the experiment the technology was limited to six materials, the number used here.

Table 2 Set of photo-polymeric materials used in the experimental data collected by Objet Geometries Ltd. (2010)

This printing technology that operates with light-hardened resins was initially developed to create fully functional prototypes in the field of product design. In the printing process two source materials (“full cure materials”) that occupy opposite ends of a material spectrum are blended to form four additional materials (“digital materials”) with graded properties. The spectrum of materials can blend between varying colour gradients, translucency or elasticity.

The materials are pre-mixed and cannot be adjusted by the user in their combination ratio. Gradual distributions with user-defined material gradients are still not feasible. Once this technological hurdle has been overcome the process can be synthesised with heterogeneous solid modelling to open up a new research field with fewer geometric constraints.69 During the printing process a seventh material is ejected from the nozzles and hardened by a punctual light source that serves as a support material to stabilise overhanging geometries in the printing process. This hardened support material must be removed in a post-printing process that utilises pressurised water, thus challenging the geometrical complexity since fragile model parts can be harmed. The mechanical qualities of this support material were not tested as a potential seventh print material in this experiment by the author, but research that implements these materials as active materials has been documented (Milos et al. 2010). The manufacturer provides the user with a selection of material properties. In the different pre-mixed sets of print materials the company unfortunately does not supply an identical selection of all mechanical properties. Certain values like flexural strength are indicated for some pre-mixed materials and not for others. In the experiment we use a pre-mixed selection that spans between VeroWhite (Full Cure 830) as the stiffest polymer and subsequently decreases in rigidity to TangoBlack (Full Cure 970) as the elastic counterpart.

A graphical analysis (Ill. 96) of the physical properties of the different print materials provided by the company points to potential mechanical inconsistencies that must be accounted for to ensure correct analysis of the material sample. For this reason two charts of the “tensile strength” and “elongation at break” values have been plotted that

This aspect refers to the point that the material complexity can be expressed with distribution functions within a given geometric envelope that is based on calculus and not on an assignment of discrete mesh-based geometries.

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identify the elastic behaviour and point of rupture. The two selected categories displayed in the graphs are the only material properties the company lists for the entire group of materials and are therefore selected for analysis.

An inspection of the curves reveals that no interpolation of the values based on neighbouring values can be undertaken without a severe risk of errors. Since we have to assume that the material variation from stiff to elastic is achieved by a gradual shift of the mixing ratios, quasi-linear decreases in the values can be expected. Since the exact blending ratio remains unknown we have to include a certain deviation from a linear curve. The two curves nevertheless show non-linear behaviour of specific digital materials that can impact the performance of the orchestrated material behaviour. The distribution of the elongation-at-break values shows significant irregular values for the material DM_8130. The noted value, which identifies the moment of rupture in an element under strain, exceeds that for its neighbouring materials with more elastic properties by over 20 % and represents the highest value in the overall scope of all materials. This irregularity can therefore affect mechanical performance in areas where there is a higher accumulation of this blended material. These irregularities must be kept in mind for a later analysis of the physical test results.

Ill. 96 Physical properties of the print material (VeroWhite-TangoBlack)

In contrast to the previous property, the distribution of the tensile strength values is more natural, with a nearly linear distribution from stiff to elastic. If we assume smaller deviations in the blending ratio between the two source materials than the expected 25 % steps, this curve appears close to normal. These deviations between the two listed mechanical properties are surprising since the values are extracted from similar analysis procedures that involve testing the elastic behaviour through elongation or strain forces. Since no clear indication of the mixing procedure and the respective ratio of the blending of the two polymers is given, an explanation can only speculate about such possibilities, as for example irregularities in the molecular bonding in specific ratios that compose the DM 8130 material. Since the list of material properties is different for the individual blends, further irregularities can be expected. In the analysis of these values one should not forget that the technology was developed to create not digitally calibrated materials, but rather physical models with realistic haptic features. The given samples provided by the company for the individual blends deliver a reasonably accurate physical impression of variation in the flexibilities needed by this envisioned application.

To determine the exact mechanical properties of the individual materials, mechanical testing of the respective fully cured and digital materials should be performed to liberate the study from the values provided by the industry. As stated before, the experimental set-up serves as a proof-of-concept for the additive fabrication of a three-dimensionally graded material with relational dependencies within the zones of the test sample. The combination between haptic tests and collection of the given values is expected to deliver results sufficiently accurate for this purpose. Yet the future calibration of arbitrarily structured and 188

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composed materials in the dimensions given by the manufacturing technology will still have to collect a user-defined set of mechanical properties to deliver a reliable result. One can only speculate that future developments of this technology in the direction of rapid manufacturing will adjust these values for more coherent physical behaviour.

Despite the limitations discussed, even today the described additive fabrication technology nevertheless can help to develop and test workflows for the physical design, configuration and description of graded three-dimensional material distributions if we accept the above mentioned irregularities. The research goal is to develop a proof-ofconcept specimen that allows physical testing and is intended to justify the developed design method and the creation of a material with a three-dimensional graduation of stiffness values under the above-mentioned constraints and irregularities.

5.2.6 Analysis of the specimen The additively fabricated specimens were examined in a mechanical test at the Institut f체r Kunststoffverarbeitung (IKV) of the Rheinisch-Westf채lischen Technischen Hochschule (RWTH) in Aachen. The mechanical analysis applied a test method that followed the DIN (Deutsche Industrie Norm) procedures listed under DIN EN ISO 60470 and was conducted on a Zwick 1456 /20 KN materials testing machine (Ill. 97). In the testing procedure the sample was placed between a base plate parallel to the surface and a circular-shaped compression tool. The sample object was then compressed at a uniform rate. The maximum load of 250 N was recorded along with stress-strain data. An integrated extensometer was used to determine the modulus of elasticity. The measurement was taken at the three locations of differing vertical forces defined by the FE model.

Ill. 97 Experimental set-up for collection of stiffness values

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Plastics - Determination of compressive properties (ISO 604:2002); German version EN ISO 604:2003 189

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For the measurements a metallic stamp with a diameter of 10 mm was manufactured, corresponding to the force insertion area of the FE model. This stamp was then gradually lowered onto the specimens at the three positions of the vertical forces assigned by the FE model. The vertical stress force applied was limited to a value of 250 N. The employed testing device plotted a graph of the resulting stiffness values divided by the ratio of vertical force [N] (“Kraft N”) and the resulting deformation in millimetres (“Weg in mm”). Before actual measurement a reference measurement was taken. Three test blocks with changing vertical forces on the identical position were made and tested accordingly. The insertion points were labelled A, B and C and had forces assigned between 600 and 100 N.

Ill. 98 Distribution of the stiffness values and assigned vertical forces

Mechanical analysis of the test samples The conducted mechanical test delivered significant differences in the stiffness behaviour of the individual specimens that correlated with the vertical deformation implemented in the specimen-specific FE method. Therefore it was possible to identify locally changing E-modules. In the individual design set-up the highest force value yielded the lowest stiffness while the lowest one produced a locally stiffer material. The individual curves show similar characteristics in all of the graphs. In test block 3 the vertical forces B (100 N) and C (150 N) delivered stiffness values that correlated with the forces applied at the test points fairly accurately. The course of the values at position C in all curves showed properties that did not fully correspond to the envisioned stiffness distribution. It is estimated that these values of medium stiffness are composed of a higher amount of DM 8130, a print material with medium stiffness values, and could be affected by irregularities in the elongation of break values (EBV). The official test

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procedure71 for determining EBV values stretches a material through a bilateral application of strain forces until the material reaches its point of rupture. In the test conducted here a material is compressed with a stress force from both sides until material failure is observed. The values we can gather from these two mechanical properties are therefore related. The previously collected information on these mechanical properties, with a special focus on the abnormalities in the EBV given by the producer of the material, could explain why these irregularities can be observed in the middle curves.

All curves show very low stiffness values in the beginning of the test phase around an applied force range of 0-50 N and proceed toward higher stiffness values when the force applied surpasses the 50-N boundary later in the experiment. The analysis graph visualises this behaviour through a slope change in the beginning. It is conjectured that this phenomenon derives from the compression of the very elastic matrix geometry material (TangoBlack) that encompasses the individual spheres embedded in the matrix. At the point of contact between the horizontally arrayed layers the local stiffness value increases as the vertical forces are transmitted between the now compressed encapsulated spheres, which are fabricated with stiffer materials than the matrix. This curve also suggests that a force-specific distance can be modelled to allow a delayed release of the stiffness values through a graded definition of the matrix material.

Radiological analysis of the test samples After the mechanical tests a radiological examination of the composition of the material was undertaken to reveal the internal structural composition and seek matrix deformations that could prove the sloping effect on the test curves below a force value of 50 N. The test was expected to gain insight into the areas where material deformation took place. For this purpose the Federal Institute for Materials Research and Testing (BAM) executed a radiological screening (Computer Tomography, CT) employing universal tomography with X-ray tubes72(Ill. 100). This technology measures differences in the material’s density and delivers a visual result of such differences.

BAM describes the functionality of such testing devices as follows: “The principle of computed tomography (2D- and 3D) is shown in Ill. 99. The sample will be turned in the X-ray cone beam and using a line detector or an area detector. A single cross-section or a multitude of cross sections are measured. Each pixel of the 2D- or 3D-image matrix corresponds to a volume element (VOXEL). Computed tomography provides a measure for the absorbed X-radiation averaged over one voxel, the material dependent linear absorption coefficient µ (unit cm-1). Usually this quantity is normalized to 8 or 16 Bit grey levels in the tomograms. To distinguish different materials, pseudo color representations are often chosen. For a fixed material composition the absorbed X-radiation is proportional to the density of the materials.” (Bundesanstalt für Materialforschung 2006, 2)

Ill. 99 Left: computed tomography with a line detector, right: area detector (Bundesanstalt für Materialforschung 2006, 2) Testing procedure described in EN ISO 527-1.

Technical specification of the applied computed tomography apparatus with X-ray energies can be found under Bundesanstalt für Materialforschung (2006) 191 71 72

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Since the specimen consists of six different polymer types with varying mechanical properties, it was estimated that differentiation would be possible through such an analysis.

Ill. 100 Left: CT image of vertical section through specimen, right: set-up of the radiological screening

The radiological tests conducted with an area detector (Ill. 100) showed very low differences in the densities of the six photo-polymeric materials. Gradual variation of the internal composition was vaguely detectable but did not deliver a result sufficiently accurate to allow reliable achievement of the envisioned visual analysis goal. It is estimated that the variation in the absorption properties of x-rays within the different print materials is not differentiated enough to allow more detailed visualisation of the heterogeneous internal structure.

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5.2.7 Conclusion An examination of the tectonic principles of functionally graded materials was valuable for an understanding of useful structural compositions and allowed their application to the realm of additive fabrication. The methodological approach that projected knowledge from material science delivered insights that could be transferred to the geometrical set-up of the test specimen based on principles for the two-dimensional material distribution of metallic materials. The presented experiment proved further that finite element analysis software can be actively engaged as a design driver to create heterogeneous material properties materialised with additive fabrication technologies to a reasonably accurate degree. The variant approach that the digital workflow was following in an adapted manner was applicable and structured the process in a meaningful way. In contrast to the previous experiment, differentiated mechanical performance was created through a computational process of sorting molecularly differentiated polymers that delivered acceptable degrees of relative elasticity between the individual positions on the test sample. The combination of both structure and material selection remains a research topic to be explored in the future.

Future research issues can also be found in improving computational speeds for the calculation of such structures, a factor that will become vital for design and analysis processes in larger scales. The test piece contained 30,000 individual spheres embedded in a matrix material. This naturally leads to a high number of mesh-faces within a relatively small model. The resolution of the spheres was therefore reduced to a number of 128 individual meshfaces to give a reasonable approximation to the original spherical geometry. Since the spheres are embedded in a matrix that also requires an identical face count, 256 overall faces were needed to describe the air-tight structure of a typical cell. Geometric operations like Boolean subtractions present significant problems for the process of modelling the matrix material due to the high number of polygons and can only be handled in segments by specialised software applications like MAGICS (Materialise NV 2010) that can efficiently compute large amounts of meshed data. Research is underway to develop different methods of geometry description like volumetric modelling, which have seen first industrial spin-offs such as Uformia’s Symvol plug-in for Rhino3D (Uformia AS 2011) that allows the design of micro-structures. Helpful in this regard is the direct export of the layered information, which is already possible today from Rhino via *.cli or *.slc file formats. This process skips meshing procedures and extracts sectional fabrication information directly from a NURBS surface or polysurface. These line-based files create an automated Boolean operation without having to join volumetric geometries and reduce the calculation to a twodimensional operation. The quality control of such files is an additional challenge since it requires laborious inspection of the individual lines before they can be transferred to the fabrication devices.

Transferring the collected FE data to the digital model is feasible, yet computational modelling issues continue to pose a challenge that limits the size and accuracy of components created by FEM. Further investigations could include generative approaches for goal-based design processes to calibrate arbitrary materials with non-linear behaviour. Contemporary research conducted on the coarsening algorithms of the linear and non-linear behaviour of materials by e.g. Kharevych et al. (2009) and others will be substantial in solving these issues and must be integrated.

The small-scale test samples manufactured here would generate files over 300 MB in size and require laborious preparation before printing could take place. An additional FE analysis of the resulting multiple material geometries, as proposed by the variant approach, is difficult with the high amount of geometric data. The volumetric information in the *.stl file would have to be meshed spatially as well, thus increasing the number of calculatory elements even further. This aspect still poses an obstacle to the fabrication of larger structures on the building scale unless the geometric resolution is adapted. Since the digital design process is based on sub-dividing the digital test block that corresponds to the later fabrication model, a fair relation between resolution and the feasible spatial mesh has to be 193

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devised accordingly. Finer analysis meshes give more accurate results, but require more cellular elements that have to be modelled and meshed. The method proposed here operates as a design tool for a defined load scenario from which the material distribution can be distilled. The geometric position of the applied structural boundary conditions is fixed and does not cover dynamic load scenarios.

An industry-independent library of additive fabrication material properties could be useful in creating more accurate testing scenarios and FE-based design process. These have to include the fabrication-induced anisotropic properties of the print materials.

Future research is required on mechanical behaviour on the cellular level. The spherical geometry chosen here appears beneficial to avoid peak loads in the cell-to-cell relation, yet costly in the number of mesh-faces required, which significantly increase the overall file size. The experiment also showed that the encompassing matrix can serve as an additional design parameter since a general tuning of the elastic properties over time can be achieved.

Building-scale solutions for these material properties require a distinct additive fabrication process with corresponding scale, accuracy and material robustness to allow the fabrication of components with a reasonable lifespan. The creation of mega-scale printing solutions for compressive load-bearing functions has seen some progress in recent years, yet a comparable technology for the creation of multi-material components has yet to develop, although it has been identified as a valuable research field for the future (Bourell, Ming and Rosen 2009, 13, 17).

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Experiment III: Multi-level Design of Textile Structures with Controllable Material Performance

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5.3.0 Introduction The following chapter relates a series of experiments that investigates the implications of new design processes that can be realised using additive fabrication tectonics. The experiments test different allocations of structure and form-defining input sources to prove that, by deploying them in different process locations, a topologically encoded structural matrix can be activated and shaped in numerous ways to deliver an innovative morphological result. The tests conducted work with a spatial system of interlocked linear elements whose assembly sequence is derived from textiles. Computational translations of textile geometries are tested in digital and physical models and geometrical constraints of these techniques outlined. The chapter delivers an argument that such multi-layered design processes unfold a novel design practice in which multiple formgiving parameters can be combined in a spatial tectonics that is negotiated through a material performance and opens up new territory for spatial and formal pre-conception in the design process.

Section 4.3 Literature Review Research Topic III discussed the impact of the projective geometry that emerged in the Renaissance and led to an expansion of the available geometric systems within architecture that had relied until that time on a Euclidian understanding of space that was reflected in the design process, materialisation and relationship between the architect and the artefact. It was argued that in contemporary computational design these streams of design engagement between the architect and his design subject were further altered in favour of an indirect relationship driven by new geometric protocols and the successive incorporation of material engagement.

The promises of additive fabrication in this realm consist in an emerging possibility of defining material characteristics through the control of structure and internal composition and its correlation with digitally encoded variant and complex geometric information that reflect new spatial concepts of architectural formgiving. The preconception of a distinct form and space that guided the architectural design process historically has now been expanded to encompass a broader formal domain that negotiates dynamic material and geometric materialisations and includes morphological multiplicities.

The contemporary designer’s interfaces that guide the final creation of a structure’s composition are highly abstracted. Spatial boundary conditions are represented through points, lines, surfaces and coordinates and formgiving information is manifold in its resources. Geometrical output can achieve a high degree of spatial complexity as the designer adjusts the individual parameters and the way they interact within the final spatial envelope. These solutions can now be teamed with additive fabrication to expand a computational design process with specific material properties. The tested utilisation of flexible materials can create structures composed of geometric encodings of their spatial connectivity, but at the same time allow material-dependent form-changing potential to be activated.

Taking these above-mentioned aspects into account, textile structures appear to be an attractive example for encoding, visualising, manufacturing and testing such composite design systems. The systematic and geometrically controllable nature of the individual threads makes the computational translations feasible in the field, while presenting an interesting application for additive fabrication techniques due to the high amount of detail they can achieve, highlighting the key advantages of this technology which allow local variations and changes in multiple materials. Local calibration of each thread’s course could even expand upon the usual control possibilities in textile manufacturing by offering a different fabrication technology with different constraints and possibilities. Textiles can visualise the conceptual implications of this design process that interweaves computational geometry and dynamic material performance by re-defining architectural form. Designing with such parameters defines topological relationships that enable an intensive performance which can be then actualised within temporary tectonic formations. Spatial, mechanical and dynamic inputs negotiate the intensive properties and create local and emergent morphologies that interpret the designed content through varying transient equilibrium states of the material.

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5.3.1 Geometry, fabrication and material constraints The digital translation of textile assemblies and their layered fabrication creates structures that resemble classical textiles but are endowed with very different mechanical properties.

Classical textiles are composed of textured73 or filament yarns that define the usability of the product to a high degree.

Multiple filaments that compose the final yarn contain structural properties with anisotropic behaviour. The structural qualities in the longitudinal direction of a yarn show higher tear resistance, whereas lateral properties are mechanically weaker. In the longitudinal direction the forces go along with the filaments’ orientation, whereas lateral properties operate orthogonally to the filaments’ orientation and produce momentum forces with bending behaviour on the filament level. Individual three-dimensional configurations of a yarn’s geometry and the material’s molecular structure amplify or decrease the specific structural properties.

A yarn’s resistance to the bending momentum that occurs while the material is assembled in space defines the threedimensional appearance of the created textile. Yarns that form a slope receive different mechanical loads and compressions at different locations within the textile until they reach the state of structural equilibrium. In each local situation structural forces are observed that try to resist bending the yarn into shape.

The mechanical relationship between the curvature, bending moment and flexural rigidity can be expressed as such: k = M/EI with:

k= curvature 74 M= bending moment 75 EI= flexural rigidity76, 77 The interconnections between the different physical and mechanical properties define continuously varying morphologies that bear the traces of the material employed, the achievable curvature of the yarn, and forces that interact on the textile. Lower flexural rigidity releases lower achievable radii of the knitted yarn, whereas higher forces interacting with the textile can force an increase in curvature until the elongation at break value reaches a critical state that causes material failure. In knitting processes these additions of local resistance in different degrees, combined with the chosen cellular patterning, restrict the three-dimensional shape of a textile. Different yarns that are knitted in equal patterns thus deliver alternating three-dimensional morphologies.

Additively fabricated structures and classical textiles differ in the material tectonics behind their assembly. In an additive process, resistance against bending momentum is based on the vertical disposition of the layered material.

Additively fabricated yarns are constructed in situ and deliver weaker structural resistance to the form they occupy since they are printed in a state of structural equilibrium.

Textured yarns are composed of heat-formable materials that can be mechanically altered for better and enhanced performance and functionality. For a good overview on the different technologies and types of yarns see Eberle et al. (2008) 74 A definition of curvature can be found in Lockwood (1963, 193) “the circle of curvature at a point P of a curve is the circle that fits most closely to the curve at that point. The centre of curvature and the radius of curvature are the centre and radius of that circle.”

75 A definition of bending moment can be found here: “the bending moment in a beam at any section is the transverse moment tending to cause bending of the beam in the plane of loading” (K. L. Kumar 1998, 197). Moments define the relationship between a force and the cantilever around a point, that tends to cause rotational motion by a body (on this see K. L. Kumar (1998, 75) 76 Equation in Smith and Chen (2008, 202) 77 EI can be defined as such: “Flexural rigidity is defined as the force couple required to bend a non-rigid structure to a unit curvature” (Landau and Lifshitz 1986, 42). It is composed of the material-specific elasticity module and the second moment of inertia that can be extracted from the cross-section of a beam.

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Since these yarns show no structural continuity that is correlated to the paths of the individual threads, the artefact exhibits different mechanical performance as it changes form. In an additive fabrication system operating only on the z-axis, anisotropic behaviour affects the yarn in changing positions within the geometry, depending on the course of the line. As a result of these fabrication principles structural weaknesses and strength change continuously within the printed geometry (Ill. 101), posing additional challenges.

Ill. 101 Left: material distribution within a yarn, (right) additively fabricated yarn geometry

Additive fabrication creates physical approximations of digital models, whose accuracy depends on the geometry’s curvature in relation to the build orientation and layer thickness. Lower curvature in the build direction releases a staircase effect that visualizes the layered process and leads to irregular material distribution over the course of manufacturing the yarn. The textile yarn, in contrast, operates with a constant radius78 over the course of its spatial path. For a later architectural application these constraints of additively fabricated structures must be taken into account in identifying the minimum thickness of the digital yarn with regard to the overall geometric complexity, which, in turn, must be adjusted to accommodate the applied fabrication technology, material and scale. These parameters deliver minimum dimension constraints of the printed artefact to ensure sufficient stability and tearresistance. These aspects have to be coupled with potentially harmful post-processing procedures to remove support structures that use such methods as spraying with high-pressure water, which and can destroy thin tubular geometries. On the other hand, increasing a radius to counteract these dangers can lead to intersecting geometries, entwining parts that should be kept volumetrically independent.79 This aspect affects the relationship in the digital model between minimum cellular size, geometry curvature and the scaling range of the threads’ performance on a cellular level.

All of the tests conducted here are designed for the available sizes of polymer-based printing technology, but a future increase in print size will reduce the risk of potential intersections of tubular geometries by altering the relationship between tube diameters and cellular dimensions that are structurally viable. The larger the print size, the smaller the tube diameter can be become in relation to the overall dimensions. Taking these aspects into account the design methods presented here can deliver fully dynamic and non-intersecting geometries from cubical cellular sizes above 2 cm3, if we take a diameter of 2 mm to be the practical minimum for the tube’s radius.

78 This is a simplification for the sake of clarity. At intersection points where the circular section is subjected to stress forces the geometry is morphed into an approximated elliptical or racetrack shape.

79 In the case of an application of these assemblies for rigid structures, the number of intersection points can be tuned by the cellular height.

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Ill. 102 Relationship between cellular size and tube diameter

In the following experiments no computational solution to all of these geometrically and scale-dependent issues will be attempted. Instead the focus is on design interfaces that can steer a process for pliable and fixed geometries that employ spatial textile connectivity systems. The solution proposed here gives full functionality for the development of textile structures on the level of the yarns’ system line. Further research would have to merge additional mathematical constraints (Ill. 103) into the spatial definition of the yarn.

Ill. 103 Peirce’s model for plain woven fabric (Chen 2010)

For a future research process on the larger-scale additive fabrication of textile structures the thesis advances the following geometrical boundary conditions that should be maintained to ensure full material performance after the finalisation of the print.

The following design aspects have to be embedded in the implementation of the geometrical model: 199

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1. Correspondence between the overall scale, material and support structure removal procedures 2. Choice of cellular sizing proportionate to the envisioned radius of the digital yarn 3. Course of the geometry defined to avoid sudden curvature breaks The textiles described here differ from conventionally industrially fabricated materials in the uniqueness of local differentiation that can be controlled with parametric CAD modelling and additive fabrication methods. As mentioned above, these technological boundary conditions leave deep traces in the way these materials operate mechanically on the level of the individual thread and how they transmit this behaviour up to the structure as a whole. The scalability of this design method can benefit from technological advancements, since all of the spatial descriptions define topologically constrained cells that can easily adapt to new geometric formats. Through the expected proliferation of technological boundary conditions it can be expected that the direct relationship to the original textile tradition practiced in this research will start to fade in favour of an augmented type of structural assembly that incorporates pliability, dynamic structural behaviour and sensitive form-changing properties with a tailored specification derived from the new fabrication environments of digital manufacturing.

Vector and coordinate-based line definitions For the definition of the different textile behaviour expressed through parametrically driven, line-based components arrayed in a lattice structure, two general models of geometric description can be applied that deliver different degrees of freedom to the movement of the line and provide diverse interfaces to implement formgiving information during the design process (Ill. 104).

The vector-based approach allows the line’s end and/or start point (or both) to be positioned along the course of a pre-defined vector spanning between these points. Advantageous for this method is the ease of definition of the individual spatial constraints, which also gives a simple interface for alteration and the removal of facile errors, but precludes three-dimensional freedom of movement of the individual point.

The second method, which operates through a tunable description of the spatial coordinates within the cellular component, provides the course of the line with more degrees of freedom. External data can be implemented to drive the x, y, and z behaviour within tunable geometric ranges that can be individually configured by numerical data.

This sensitive differentiation can thereby express stronger axis-dependent reactivity derived from a definition of numerical ranges that has to comply only with the connectivity parameters of the chosen textile assembly.

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Ill. 104 Vectors and coordinates for tunable encoding of line elements

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5.3.2 Weaving Means of textile assembly like weaving, crocheting and knitting operate through a constrained performance of single (crocheting and knitting) or multiple (weaving) linear elements whose connectivity is maintained under changes in form. This section focuses on the general geometric connectivity systems of weaving and knitting; the additive fabrication of other forms of textile structures like braids, lacing, crocheting, plaiting are also conceivable, but will not be treated in this text. The reason for their exclusion lies in the characteristic mechanical differences between the two textile systems that affect their form-changing potential.

Weaving is one of the oldest “industrial art[s] practiced by primitive cultures” (Todd 1902, 20), traces of which have been found in Central Africa, Mexico, Israel and the Pacific islands among others. The Egyptians invented the first looms that operated in a horizontal and vertical position, which would later become became a key textile technology during the industrialisation of the 19th-century Europe.

A classical description of the weaving process is given by Dooley as follows: “In order to understand the different kinds of weaves it is necessary to know […] the process of forming cloth, called weaving.

This is done in a machine called a loom. The principal parts of a loom are the frame, the warp-beam, the cloth-roll, the heddles, and their mounting, the reed. The warp-beam is a wooden cylinder back of the loom on which the warp is wound. The threads of the warp extend in parallel order from the warp-beam to the front of the loom, and are attached to the cloth-roll. Each thread or group of threads of the warp passes through an opening (eye) of a heddle. The warp threads are separated by the heddles into two or more groups, each controlled and automatically drawn up and down by the motion of the heddles.” (Dooley 1914, 53).

During the weaving process two separate yarns are interlaced with each other to compose a fabric structure. The threads that run lengthways are called the warp, whereas the orthogonally opposing thread is conventionally called the weft or filling. Patterns are created by a rhythmic and geometrical course of the weft yarn that is contrived in differently spaced positions of the warp organised around the warp beam. Through this method selected vertical movements of the warp are entwined with the horizontally threaded weft yarn, which combine to create a flat spatial structure and allows pattern variation based on a graphical encoding (Ill. 105) of the vertical weft movement.

Ill. 105 Left: Kilim weaving pattern, right: patterning with warp and weft yarns (Todd 1902, 47)

Several traditional patterns are known and have been practiced over centuries. The most prominent are called the plain, basket, twill and herringbone (Ill. 106). All variations are defined by the selected movement of the warp 202

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threads, which can be described numerically. The patterning can be represented by the number of warps and their location in the z-axis for two or weft lines as follows:

Ill. 106 Weaving patterns and warp sequence (Todd 1902)

Weaving delivers textiles with isotropic material behaviour in the x and y-axes due to a straight connection between the intersecting points that appear where warp yarn in the x-direction interlaces with horizontal weft yarn in the ydirection. The weaving technique operates from a planar surface whose perimeter is given by the loom’s dimension and is structurally defined by the interlocking of the warp and weft threads. The applied pattern defines the pliability of the textile through more or less densely woven interconnections between the individual threads. Local pattern variation of a digital woven geometry can define local pliability control, which can be achieved computationally by sorting an Excel spreadsheet responsible for the pattern generation.

Knitted structures, on the other hand, are characterised by a curvilinear connection between the intersections of stitch and purl. This over-length of the yarn is responsible for significant anisotropic changes in form in the x, y and z-directions. The woven plaid that leaves the loom can be understood as an approximation to a flat surface with openings created by the pattern. The knitted structure, on the other hand, operates more spatially, as shortenings of stitch and pearl, perhaps coupled with specific knitting patterns, define a configuration that contracts or expands the spatial system and delivers a highly three-dimensional structure.

Computational translation of weaving patterns In order to test a geometric workflow that can generate digitally controlled weaving patterns reactive to external formgiving information and spatial boundary conditions, the modelling process displayed in Ill. 107 has been devised.80 This workflow, which will also be applied to the knitting example, starts with an analysis of the local threads’ spatial behaviour and their systematic interlocking modus as an arrayed spatial assembly. In the next step local variations of these rules can be parameterised to represent patterning information. These individual cellular elements are spatially defined so that they can be adapted to the local cellular boundaries, but rigorous in complying with a structural system that defines the logic of the individual textile. In accordance with the patterning systems, different combinations of these individual cells can be assembled. The character of this relational description is topological, allowing structural continuity of the distinct textile properties regardless of scale and under extreme The experiment developed here employs the Paracloud software (Nir 2009), an Excel-based parametric design tool for the geometrical configuration of cellular geometry.

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changes in form. These parametric definitions of the cells provide only relative movement control, which has to be actualised in the distinct spatial conditions of the final design task.

In the modelling process these components populate a cellular array that is created by monotonous or variable offsets of ordered point clouds, line networks or NURBS surfaces. For the modelling of the yarn’s course, simple line segments with variable end points are employed. The method applied for the topological description of these points is based on the coordinate model, which allows three-dimensional flexibility within a relative spatial range.

The movement of the individual yarn’s end points is defined by a scaling range for x, y and z-coordinates that is adapted proportionally to the final cellular sizing.

The following knitting experiment presents a description of how design processes can utilise different possibilities to drive geometric interaction, shows the definition of different cellular stitch topologies, and highlights the design interfaces for a spatial assembly of such.

Ill. 107 Diagrammatic modelling process applied for digitally woven structures

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Example 1: Digital modelling of a plain weave In the first test a plain weave pattern will be computationally defined consisting of alternating movements of the weft yarns above and below the warp thread. The system of weft movement can be described in regard to the individual rows of the weaves as follows: Warp movement: Initial Row: Over 1, Under 1 Next Row: Under 1, Over 1 This pattern can be used to define linear geometric elements (Ill. 108) in a following fashion: Only a limited amount of spatial information within the individual cellular elements is flexible, whereas other elements have to remain constrained to ensure the integrity of the weaving system under deformations.

In the example of the warp thread of module A, spanning between 0 and 1 in the x-direction, one can see that z-axis movement is generally allowed within a certain ratio defined by a constraint value that ensures a minimum spatial difference to the weft line, while x and y-axis movement is locked. The final position of the variable numbers is then encoded by a single value or contains individual cell-specific geometric information tailored by a scaled numerical matrix or a single value for the warp or weft line. Alteration between the two cell types can be achieved solely through exchanging the scaled values of the zcoordinates of the line’s mid-points. In our case the variable z-value of module A’s weft line can be applied to the variable zvalue of the warp element in Module B and vice versa to achieve the desired weaving structure.

Ill. 108 Left: Plain weaving pattern, Module A-over 1: right: Module B-under 1

Pattern definition and cellular height Following the pattern instructions that traditionally define the plain weave, a cellular distribution sequence of alternating modules A and B is achieved. Patterns are controlled by an Excel worksheet in which each assigned 205

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numerical value represents a cellular unit (Ill. 109). In a next step the distinct height of the cellular lattice can be defined as a constant or changeable value and hereby embed spatial information and three-dimensionality. In order to demonstrate this ability a gradient pattern is chosen in which colour information is transferred into numerical cellular offsets. This cellular variation allows a computational calibration of surplus material that cannot be achieved with classical weaving systems. Due to the significant heights of the individual cells, the lengths of warp and weft are differentiated accordingly. Since these values appear in form of an Excel spreadsheet, this property is easy to scale and thus the pliability of the material can be calibrated to differ locally.

Ill. 109 Left: Plain weave modular distribution pattern, right: gradual offset pattern for definition of cell height

A gradient pattern was chosen for this example, yet a broad bandwidth of steering matrices can be applied as long as they comply with the Excel framework. Visual data created in an analogue or digital process can be easily transformed into numerical values. Excel itself can be employed as a direct programming interface to create intercellular dependencies and derived values that can be scaled and represented graphically.81 The numerical values can be retrieved by scaling the initial matrix that was responsible for the offsetting of the individual subsurfaces, by assigning fixed values, or through a whole new set of numerical values that are created elsewhere. In our case we chose to scale the initial Excel spreadsheet (with gradient numerical distributions) that defined the offset.

After the setup of these instances defining the weave’s geometry, the two-dimensional pattern can be modelled and controlled. Since most of these instances are defined by relational values, flexibility and adjustment can be maintained throughout the process. As stated above, individual input sources can be applied in numerous locations within the design process to interlink dependencies in different parts of the morphology. The combination of formgiving information defines an abstracted interface through which artistic activity can take place and provide significant possibilities for design evaluation and conceptual translation. Weaving in numerous fields of graphical and numerical information into one design procedure represents a novel interface for creative engagement and geometric control of material performance. The definition of these aspects then delivers a three-dimensional course of a plain weave with subtle changes in the warp and weft paths (Ill. 110). In the illustration, different lengths of threads teamed with the gradual offset of the root surface become apparent. These aspects of computational formgiving, which allow the control of a high degree of local information, represent an expansion of traditional weaving systems.

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The knitting example shows how cellular automata patterns can be used for this purpose.

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Ill. 110 Left: 3D model of a plain weave structure with local gradient of the weft and warp length, right: gradient map

Example 2: Digital modelling of twill weave The next test shows that the proposed modelling methodology allows pattern variation with structural correspondence to be implemented by digitally controlling the yarn’s surplus length. This presents another interface for design engagement and the creation of bespoke material properties. To test the feasibility of this method, the modelling of a twill pattern will be studied.

In this woven structure the weft yarn continuously passes first over two warp threads and then under a single warp thread, with a “step� or offset between rows to create the characteristic diagonal pattern. Each pattern line is performed twice in the process. The fewer interlacings of the weft allow the yarns to move more freely and thus create a softer and more pliable textile. The test uses parametrically defined shed heights and a related density of warp and weft intersections. The differentiation of the weft heights provides varying surplus lengths of yarn, as we saw earlier and is complemented by the relative density of weft and warp cells that amplify this effect even further.

This varying cellular sizing can be further controlled by placing additional attractor points (Ill. 111). These were located in the centre of area experiencing maximum deformation in our example, but can be placed arbitrarily. The control points exert a translation of the x and y-positions of cells that can be tuned in size and intensity of effect.

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Following the methodological approach, existing knowledge derived from the historical craft of weaving can be implemented and mapped onto contemporary fields of computational design. The abstracted pattern encoding used in classical weaving can be translated and computationally expanded through enhanced geometric control of the virtual yarn and gradual variation of shed heights difficult to achieve in conventional processes. Geometric translations of various inputs can be implemented since the digital weaving process relies on the tectonics and build processes of additive fabrication rather than on the mechanical boundary conditions of the classical loom. The experiments do not attempt to copy these textile procedures, but rather use them as a source for innovation that evolves out of innovative computational and fabrication principles. This approach thus promotes the application of computational models for compressive structures as well, since the interlocking linear elements can create a shell-like surface82 with multiple openings that cannot be achieved with classical weaving procedures.

Patterning sequence twill weave Analogous to the previous experiment, this experiment starts with the classical description of the patterning sequence characteristic for twill weaves, described as follows: Warp movement: Initial Row: Over 2, Under 1 etc.

Next Row: Under 1, Over 2 etc.

The pattern assortment of the twill weave can be translated into an Excel spreadsheet as shown in Ill. 111. The numbering references the previously defined weaving modules in a different order.

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On this see the test conducted by the author on a vaulted grid shell, shown in chapter 1.1.3.

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Ill. 111 Left: module distribution in a twill weave, right: grid distortion with a gradual decrease in x and y-values

The position of the attractor points A1 and A2 can be paired with a colour map that releases z-value deformation after the offset of the initial grid and hereby amplifies the density of the weave by controlling the yarns’ surplus length. After the planar grid spacing has been defined, a cellular offset can be created that forms the container for the individual modules organized by the patterning scheme. In this case the surface offsets are defined with a z-value that was extracted from an exemplary colour map, but other input sources are possible. The individual z-values can be placed in a spreadsheet and scaled to comply with a given range of maximum and minimum offset vales that are applied to the base-point grid.

This process was able to grant graded control of the individual cellular offsets, but also translated visual information retrieved from finite element processes in which load-bearing performances could be coupled with cellular density.

Applying this offset procedure to the initial surface with gradually varying grid sizes defines the following cellular distribution (Ill. 112), which serves as the container for the different modules’ spatial activity.

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Ill. 112 Twill weave pattern applied to deformed cellular matrix with gradual deformation of initial grid structure

In the modelled example, a translation of the cellular deformation in terms of height and the general dimensions of the x and y sizes are traced. The warp and weft movement can be controlled by the patterning information inscribed in the Excel matrix, and switches between twill and plain weave can be accomplished rapidly to allow the testing of multiple structural formations.

In a next step the calibration of the yarn’s thickness is investigated by a simple sorting algorithm that defines, e.g. length-specific radii of extrusion pipes. Since the modelling process creates the individual warp and weft as single lines between two control points, this data can be retrieved effortlessly.83 In the example presented here (Ill. 113) the complete set of lines was sub-divided into six different length groups that were correlated to a specific radius. These groups were then assigned to related print materials of multi-material printing technology using light-hardening polymers, which allows multiple materials to be printed with differing mechanical properties. For a mono-material printing (like SLA) the length of the line segment could be correlated individually with the assigned radius, resulting in a continuous variation of the tubular diameters. This possibilities of local calibration, one of which is portrayed here, point again to the specific benefits additive fabrication can offer to a process chain in which local irregularities to not entail an increase in manufacturing time, but are constrained only by the machine’s boundary conditions with regard to minimum geometric dimensions, layer thickness and size.

The individual lines created were joined into polylines and then modelled into spline curves by interpolating through the polyline’s vertices.

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Ill. 113 Differentiation of thread radii depending on line lengths

In this last example one can also observe that the initial weaving process is transformed into a new assembly system in which local exchanges of thread sizing and mechanical properties can be achieved, that are not realizable as such in conventional knitting procedures. This analysis of textile assembly methods thus serves as a mere starting point for an investigation of these structures with discrete cellular behaviour, whose properties can be further adapted and expanded through a deeper correlation of the manufacturing technology in the future.

These structures also can be combined with supplementary material and structural layers that can be fabricated simultaneously. Such composite assemblies, which can be manufactured in a single build process with varying materials and local geometric modifications, cannot be achieved with a time-sequenced production of textiles. One demonstration of this is the material presented here with an inner diamond structure, with varying cell dimensions and interlaced linear elements on the upper and lower levels. The course of these linear elements follows a colour diagram that was used in a previous demonstration and leads to contraction in the areas of higher stress (red) and relaxation in the lesser stressed segments (green) of the piece (Ill. 114). The fabrication of such structures that can contain multiple levels of functions and structural behaviour represents a research field worth exploring in the future, since biomorphic concepts of structural hierarchy can be embedded and coupled with dynamic performance. In contrast to industrially fabricated multi-layered textiles, these composites can be three-dimensionally complex in their

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layer configurations and interconnect different textile assembly systems that provide different mechanical functionalities.

Ill. 114 Left: Zcorp print of test geometry, right: composition of multi-layered composite

Besides mechanical performance, logistical functions can be implemented, like cooling and heating channels that are modelled collision-free in predefined segments of the cellular geometry, with spatial morphologies corresponding to their functional performance. These aspects will become more relevant and easier to research when larger fabrication sizes are achievable that allow the facile removal of support structure and better and longer-lasting mechanical performance of the print material. The poor mechanical quality of polymer-based models remains a significant problem for functional implementation, since structural deformations soon lead to weakening and deterioration of the material. In the example shown below (Ill. 115) such a material failure can be seen on a planar elastic surface equipped with stiffer cones. The more elastic base surface built in the z-direction shows cracking in the x and ydirections around the cones after just a few bending movements.

Ill. 115 Material deterioration of a composite polymer structure

The last two experiments served as investigations of computational modelling on the one hand, but also to examine multiple design interfaces that can be applied for the creation of a spatial design. The geometrical freedom from the 212

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final object that can be achieved in a remote process allows implementation of a more abstracted type of visual and numerical information. In the next experiment these aspects will be explored further through more complex patterning, and the interconnection of multiple formgiving instances with complex control mechanisms of linear elements.

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5.3.3 Experiment Preface: Digitally Knitted Structure The following experiment develops a digitally driven material formation through a precisely steerable parametric system organized by a knitting logic. Knitting operates with a single thread following a spatial cellular movement in the form of interlocking geometric entities called stitch and purl.

“Knitting may, with equal propriety, be defined as the formation of a texture of chains," the whole process being a succession of links all dependent on the first and secured by the last. Take a piece of string of any thickness and of any length—form a loop at one end; through that loop draw another, and another in succession till the string is used up; at last, draw through the end singly, and tighten it, and you have accomplished a piece of knitting.” (Copley 1849, xi - 3) Knitting is a “looping technique and the knit stitch can easily distended in either direction—known as bidirectional distortion” (McQuaid 2005, 48-49). This flexibility is due to the distinct connectivity system that differentiates this technique from weaving because material performance and three-dimensionality are controlled by a natural surplus length of the interlocking yarn on the cellular level, and complemented by the chosen patterning sequence. Weaving processes usually operate by subjecting the individual yarns to tension through the forces that are created by the warp beam, and through longitudinal planar connections. In a classical handmade knitting process the yarns are assembled without linear stress, but through the type of knitting pattern, the material and the density of the knitting process. Combination of these formgiving factors creates a distinct three-dimensional form.

“Knitted textiles are fundamentally three-dimensional. By continuing to knit on selected needles, while retaining others, a differentiation in length and in the art of binding yarns (tuck loops, floats, in-laid yarns, stitch transfer) can be created in turn, generating complex forms.”

(Ramsgard-Thomsen and Hicks 2008)The characteristics of the knitted form are maintained under the numerous morphological changes that a textile can potentially perform. These characteristics are of a topological nature, since they allow a modulation of the form while maintaining the connectivity throughout the process. The form generically incorporates alteration and dynamic movement while maintaining a defined ruleset of connectivity that is never abandoned. Along with this morphological deformability comes a broader definition of form that is defined not as a static end product, but rather as a zone of infinite but not arbitrary morphologies of unrepeatable temporal configuration. This aspect expands the term from a classical architectural conception as a more static and final materialisation of a design process, towards a territorial understanding of formal multiplicities.

In an architectural design approach this relationship between the dynamic material performance and static design of the knitting pattern allows the creation of haptic three-dimensional surfaces with pliable properties, but also offers a defined locus for design activity that accounts for the proto-three-dimensionality, density and flexibility of the structure.

Additive fabrication, in contrast to contemporary machine-operated knitting procedures, can give control of the yarns’ dimensions (structure) and mechanical properties (material) that impact the morphology of the created structures. The variability of the pliability can also be defined by coupling both properties, simultaneously adapting the yarn’s radius and material. The two previous experiments demonstrated this ability with graded composite samples and auxetic structures in which either the material or the structural composition was altered.

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5.3.4 Experiment: Computational design and additive fabrication of knitted structures Research goal The experiment conducted here creates a computational design method for knitted structures on spatial grids based on a single point, a line or a surface. The knitting encodes multiple thread configurations and allows pattern variation similar to classical knitted textiles. The computational design investigates different input sources for the calibration of the spatial configuration of the yarns. The multi-level implementation of these input sources for cellular distribution patterns, and encoding of the thread’s surplus length and local spatial behaviour, is attempted and analysed. The created design is printed as a three-dimensional model and functionality tested mechanically and visually through physical inspection. The research further discusses the potential applicability of the design process for mega-scale additive fabrication processes and compressive structures.

Applied method The experiment computationally defines topologically flexile spatial definitions for individual stitch and purl situations from classical knitting patterns. The cellular geometry is digitally encoded and tested with various patterns on multiple geometries. The experiment demonstrates different formgiving instances ranging from images to numerically encoded matrices that act structurally on different hierarchical levels of the knitted assembly. The experiment tests the impact on the formgiving instances with images, digital models and physical samples.

The methodological outline introduced earlier sees an application for this experiment in a computational translation of the intensive structural principles of textiles that is correlated with a novel manufacturing technology. As mentioned above, this mapping process entails characteristic alteration of the morphological properties of the studied textiles themselves, created by the tectonics and mechanical impact of the novel fabrication method. The research thus departs from a purely computational approximation of knitting tectonics by integrating new design interfaces that act upon the geometric content of such structures. Through the implementation of these parameters a successive unfolding of a new typology of potential building elements could be conceptualised, bearing the traces of their textile origins complemented by the emergence of new and innovative mechanical behaviour and visual presence. The experiment hereby provides the foundation for further-reaching research activities that can be achieved through technological developments in the field of additive fabrication, which can then build upon the conceptual foundations laid out in this research.

Experimental sequence The experiments are conducted in a sequence that increases the complexity of the digitally defined knitting stitches and patterning information and the applied multi-level interaction between external formgiving parameters. These experiments highlight that novel geometric protocols allow a different approach to design to be attempted, liberating the author from direct interaction with the final morphology in favour of a flexible, rich field of design spaces that regenerates their impact in varying intensities. The tests that are conducted as digital volumetric models and physical samples operate under the fabrication constraints mentioned above.

The experiments cover the following topics: 215

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1. Digital definition of simple stitch and purl geometry and application on a planar sample geometry 2. Spatial adaptation of simple knit to a source geometry with a gradual cellular offset retrieved from a graphical source 3. Application of plain knit sample geometry with distorted cellular morphology derived from a cellular automata [CA] pattern.

4. Application of plain knit on a sample geometry with varying offsets and local variation of the cellular behaviour and creation of a printed test sample 5. Digital definition of multiple knits and application on a planar sample geometry 6. Spatial adaptation of a multiple knit to a planar and spatially complex geometry with local deformation values in a patterning sequence retrieved from a CA

Experiment Step 1: Digital definition of simple stitch and purl geometry and application on a planar sample geometry The first step of the experiment creates a basic knitting pattern that is composed of three individual cells to describe a simple stitch and purl connection. The knitting connectivity is maintained through a synchronisation of choreographed linear movements in a constrained fashion. The movement is designed in such a way that structural interlocking is maintained at all times, but can vary in range to allow structural alteration to be detected. The diagram illustrates the individual point configurations (Ill. 116).

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Ill. 116 Parametric definition of plain knit

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Each component consists of six to eight individual lines in which different parts of the coordinates can be controlled. The start points and end points of these polylines are usually constrained by a fixed value in the x or ydirection to ensure linear continuity with the neighbouring cells. The formgiving numerical information is retrieved from a binary spreadsheet (Ill. 117) in which the different ranges are defined and scaled.

The numerical ranges applied can be found in the list describing the values for PM1 to PM8. In the applied ranges PM2 and PM5-PM8, the spreadsheet numbers have to be shifted to ensure spatial continuity in the two dimensions. In this process the end point value of each cell is synchronised to correspond to the start points of the following cell. Deformation potentials differ by the numerical range that can act upon the points relative to the standard cube. The maximum range is found in the PM1 data set, which can produce variations of up to 0.5 on the individual coordinates between ranges of 0.4 to 0.9. Other parameters have more modest alteration values, like PM3 or PM4. Individual ranges can be cross-assigned to the x, y and z-values of multiple points.

The deformation ranges that act upon the points from which the polyline is constructed defines the sensitivity to formgiving worksheet data. A single value releases a monotonous course of the individual cells, whereas cellular variation of the values leads accordingly to alterations of the lines course. The definition of these ranges can hereby control how strong the expressivity of the external data is translated into the final morphology.

Ill. 117 Geometric definition of a simple knit in Excel

In the next step this computational description is applied to a simple base surface offset by a constant value. The cellular definition of the individual knit lines is controlled by a fixed value within the numerical ranges. A medium value was picked for this example.84 This test is conducted to see whether the connectivity parameters of the knit components are fulfilled and operative. After all of individual lines were created they were joined and formed a single 84

Medium value means, e.g. for PM1, covering a numerical range between 0.4-0.9, a value of 0.65 was chosen.

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line. Since the created lines are defined as linear connections between the coordinates, a curve was generated through the joined polyline vertices, producing a spatial curve compliant with the connectivity parameters. The created lines were piped to create a volume.

Ill. 118 Digital model of plain knitted cells

After modelling the structure was checked for geometric intersections of the tubular geometries (Ill. 119).

The maximum radius for a plain knit in a cellular dimension of 1x1x1 units was defined as 0.035 units before an intersection of the lines would occur. In a 3 cm続 cube, a piping diameter of ca. 2 mm85 could be achieved given a medium numerical value for the positioning of the knits.

Changes in these values to more extreme rates could optimise this aspect further more since a greater lateral and longitudinal movement would take place, leading to greater distances between the individual pipes.

Ill. 119 Tubular intersection with a radius of 0.035 in a given cellular dimension of 1x1x1 .

85 A diameter of 2 mm represents the lower limit for additively fabricated polymer structures to allow the safe removal of support structure.

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Experiment Step 2: Spatial adaptation of simple knit to a source geometry with a gradual cellular offset retrieved from a graphical source The general functionality of the plain stitch has been proved and can now be applied to a more complex surface that combines pictorial and geometrical information for novel textile-inspired morphologies.

The source geometry for this test is retrieved from a height-field map (Ill. 120), a standard procedure in contemporary 3D modelling applications. The height-field information is also applied for the definition of the cellular height. Areas of the height-field surface with high curvature create a larger cellular offset, whereas flatter parts of the geometry are offset to a lower height.

A height-field map of pixel information generates a three-dimensional NURBS surface morphology based on the RGB or greyscale values of the digital image. The darker parts produce stronger z-value deformations. The accuracy and number of deformations is based on the sub-division ratio of UV curves and the maximum spatial deformation range taken from the darkest part of the image. In this example the respective UV sub-division ratio of the height-field had to be correlated with the later cellular distribution scheme to deliver corresponding sub-division ratios. Higher sub-divisions of the NURBS surface lead to greater accuracy in the mapping of the pixel information and to greater irregularities in course of the surface, whereas lower sub-divisions create a smoother but less accurate representation of the initial image material. The definition of the maximum deformation range can be chosen arbitrarily since relational values will be employed that differentiate the spatial position of each parameter point to one another. These relationships will be scaled later to deliver offset or transformation ranges in the final parametric model.

The height of the individual cells is also extracted from the surface and hereby connects base surface curvature with space for cellular movement. For this purpose the surface is rebuilt in the later cellular dimensions and the UV curves extracted and intersected. The generated points are split up into their x, y, and z-coordinates. The z-coordinate list can then be transferred to Excel and scaled to their appropriate ranges.

Ill. 120 Left: initial graphic map, middle: height-field created from bitmap, right: retrieval of z-coordinate information

The extraction of this numerical data is used to amplify and underline the general course of the surface by varying the cellular heights. In the example the darker areas of the image give higher surface-normal offsets, whereas lighter areas provide more subtle cellular dimensions. This matrix defines the three-dimensional cellular envelope for the action space of the individual knit. The retrieved value from the scaled matrix assigns a specific height value to the individual cell.

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This cellular height impacts the three-dimensionality of the structure and the flexibility of the individual knit.

Increasing cell heights allow for an elongated movement vector of the individual hinged polyline (Ill. 122).

Mechanical properties can be controlled through an implementation of these geometric conditions since the yarn’s surplus can be encoded. Offset values can be easily scaled or inverted numerically using the mathematical functions integrated in Excel. As shown before, these values can be assigned with varying length-dependent tubular radii or a choice of up to 14 mechanically differing materials using Objets’ Connex process. These aspects can potentially enhance pliability control even further and create gradual variation that is specific to both the geometry and the material.

Ill. 121 Relationship between cellular height and movement of the knit

After setting up the spatial cellular matrix, values for the initial plain stitch on the surface can be populated.

Analogous to step 1, a medium-range value will be used to configure of the positioning of the individual lines will be used. After populating the three individual components the following surface configuration can be modelled (Ill. 123). Since the correct yarn’s spatial continuity generally functions in a plain stitch, its consistency in more complex 221

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situations must be examined under differing cellular dimensions. Three cellular locations were chosen to investigate whether this structural continuity is maintained under deformations.

Ill. 122 Gradual cellular offset based on scaled z-coordinate values

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Ill. 123 Deformed surface with cellular distribution of plain stitch

Inspection at three locations reveals strong deformations in the piped knitted lines, correlated with the curvature and offset height of the cellular matrix. The systematic knitting system remained unchanged as shown in Ill. 124 and showed no volumetric intersections.

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Ill. 124 Knitting path at three sample locations

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Experiment Step 3: Application of plain knit sample geometry with distorted cellular morphology derived from a cellular automata pattern The previous test showed that image and numerical information can be used to calibrate the structural morphology of digitally created textile structures. In the following test the scope of formgiving instances will be expanded to a computational process, in our case a Cellular Automaton (CA) that can act upon the composition of the geometry and affect the mechanical performativity and emergent morphology. This applied process should be seen as a placeholder for other generative computational processes that can act upon the final geometry in shaping pattern sequences, material surplus lengths or distortion effects among others, and hereby increase the complexity of the achievable result. For this reason the text will give only a basic introduction to the chosen Wolfram 1-dimensional cellular automata.

The Wolfram 1-dimensional CA utilised here represents an elementary CA system. CA systems are “among the simplest representations of complex systems; where for the moment we may take ‘complex systems’ to mean any dynamical system that consists of more than few—typically nonlinearly—interacting parts” (Ilachinski 2001, xxvii).

Applications of resembling processes began in John von Neumann’s research on cellular reproduction and later saw applications for optimising electronic circuits to allow better checkerboard layouts on the earliest circuit boards.86 A basic definition of CA rules has been given as follows: “Elementary cellular automata have two possible values for each cell (0 or 1), and rules that depend only on nearest neighbour values. As a result, the evolution of an elementary cellular automaton can completely be described by a table specifying the state a given cell will have in the next generation based on the value of the cell to its left, the value [of] the cell itself, and the value of the cell to its right. Since there are 2×2×2=2³=8 possible binary states for the three cells neighbouring a given cell, there are a total of 256 elementary cellular automata, each of which can be indexed with an 8-bit binary number” (Weisstein 2011) Given these definitions it becomes apparent that CA develop complex patterns from rather simple starting conditions with characteristic distribution patterns over the course of their calculation process. The cellular automata are numbered according to these characteristic patterns.

In the simple CA pattern utilized here, called “Rule 90”, a single cell is placed in the middle of the top row of the matrix whose resolution corresponds to the later surface sub-division. The CA’s cell can develop the following behavioural rules:

Ill. 125 Rule 90 cell conditions 1-8 (Wolfram 2002, 25)

The diagram describes the characteristics of Rule 90 in two rows. The first row shows all eight possible conditions three cells can occupy. The second row shows the potential reactions to the neighbourhood configuration. From this simple ruleset it is apparent that the start cell (number 6 from left) can be followed by rules 3, 4, 7 and 8 (from left).

The characteristic pattern that emerges out of these few rules delivers an orchestrated distribution of black and white cells in a triangular pattern (Ill. 126). For implementation in our numerical model, the two colours were translated 86

For a full introduction to the historical development of CA see: Wolfram (2002, 876-880).

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into numeric values: 1 for black and 0 for white spaces. The numerical data of the cellular automata pattern Rule 90 consisting of 1 and 0 is collected through an output of standardised processing87 definitions exported to a text file, with rows and columns corresponding to the final sub-division of the surface.

Ill. 126 CA pattern based on rule 90

This binary matrix can be implemented in the modelling process by developing -

a patterning sequence88

-

a definition of cellular heights

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local movement control

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cellular distortion

In order to visualise the implementation of this additional source, the creation of local and gradual deformations on a cellular level will be attempted. This technique already was tested with arbitrarily placed points in the previous 87 88

Fry and Reas (2011).

Which will be shown in steps 5 and 6.

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weaving study and will be followed now with a higher number of points in precise geometric positions. These points will be configured in such a manner that after placement a contracting force should be exerted in the x and ydirections89 of the neighbouring cells. In order to allocate the two-dimensional point distribution on a complex, curved three-dimensional surface the Excel spreadsheet was used to define a pattern from which a point can be extracted.

For this purpose a line was chosen that passes from point 1 to point -1 in the notation of the cellular component. After the population of this element in a patterning sequence given by the text file, the mid-point of the connecting line running diagonally between the assigned points could be extracted. These points can then be assigned with a graded contraction force that acts upon the spatial neighbourhood. (Ill. 127). The individual numbering of the points could also be used for individually defined contracting values, but will not be attempted here.

Ill. 127 Local cellular deformation based on CA pattern sequencing

In the image shown below one can observe the contractions exerted on the final surface. Edge zones located near the pulling points are transformed, whereas the centre areas that correspond to the spreadsheet’s “0” values remain largely unaffected by the points. The fading effect of the pulling force can be seen vividly in the seam area between affected and unaffected zones of the geometry (Ill. 128).

89

x and y with respect to the curvature of the initial height-field geometry.

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Ill. 128 Top view and perspective of distorted and undistorted geometry

In the final digital model (Ill. 129) the cellular contractions resolve in smaller dimensions of the discrete performance space of the line elements, leading to a tighter knit with shorter surplus length. The contractions thus can calibrate mechanical performance rooted in the CA pattern applied to individual, arbitrarily shaped NURBS surfaces. The method shows that for the design process of complex structures a simple ruleset can be applied in a tuned manner to create a blend of interacting players that then drive the final morphology.

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Ill. 129 Final knitted sample with CA pattern applied

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Since the evolved geometry appeared rather chaotic in the constricted areas, a final test was conducted to confirm the structural persistency of the knitted structure. The inspection (Ill. 130) of a detailed area with curvature change on the root surface and changing cell behaviour revealed no failure in the conformity to the initial ruleset of the three components. This test proved that the encoded plain stitch behaviour really operates with a topological ruleset that adjusts its required spatial dependencies to arbitrary cellular dimensions.

Ill. 130 Homeomorphic transformations of cellular components under geometrical and cellular alterations

This aspect allows the implementation of the component to a broad bandwidth of complex surfaces that can be altered and distorted in the presented fashion and still operate as knitted structures as long as they comply with the given ratio of tubular diameter to cellular sizing.

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Experiment Step 4: Application of plain knit on a sample geometry with varying offsets and local variation of the cellular behaviour and creation of printed test sample In the following study locally tuned alterations of the knit component are developed and tested that provide an additional location for the morphological design of textile structures. In order to calibrate the graded behaviour on a cellular knit level, individual matrix values will be assigned to the x, y, and z-coordinate values of the constrained linear elements. Analogous to the previous examples, numerical data that drive the local configuration of these thread lines can be collected from image, spreadsheet or computational sources. These data must then be broken down into a sequenced binary matrix that corresponds with the planned cellular resolution of the final artefact. This process should lead to local spatial reactions to the input sources on a cellular level and integrate this encoded information on a morphological level that is subtle, but nevertheless detectable. Local control exerted on the level of the stitch goes beyond the control option of classical contemporary knitting technologies, but can be manufactured by additive fabrication. The effects created are seen not so much as a way of controlling surplus length in the first place, since this appears more feasible through cellular sizing, but rather as a locus for an understated mapping of external information that breaks with the geometric regularity of the thread’s course when periodic cellular heights have been chosen.

In the first step of the design process, numerical information that defines the form is generated and then applied to the offset of the initial cellular matrix, but at the same time helped encode the local movement. These values are derived from the previously mentioned input sources; in the case presented here a numerical gradient was chosen that was created from an image with a circular colour gradient (Ill. 131). For control of the local movement on the level of the knit, numerical domains were scaled to comply with the spatial boundary conditions assigned to the individual nodal points. Adaptations of these scaling ranges drive reactivity towards the influencing relational matrices, since the relative movement can be tuned on the point level. In order to control the full spectrum of linear three-dimensional movement of the knit components, eight numerical cellular domains are encoded with different scale ranges (see again Ill. 117), all of which were based on the initial form-defining numerical information. These ranges provide cell-specific numerical values to the respective x, y and z-coordinates of the linear elements. These values produce continuous spatial courses of the knitting line within the cell itself, but also ensure connectivity to the neighbouring four cells of the lattice assembly.

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Ill. 131 Scaling of binary matrix values for cellular motion control

A freeform lattice structure was created by an ordered point cloud (Ill. 132) with the cellular geometries varied locally. The cellular height of the lattice was defined in this case by the numerical information from the circular colour gradient and delivered gradually varying cellular heights. After the cellular lattice structure was modelled the correlated three-dimensional movements of the individual thread components could be controlled by the same matrix that was scaled to the line-specific numerical ranges.

Ill. 132 Root surface from point cloud

The image shown below (Ill. 133) demonstrates two knitted rows that have been extracted from the overall structure.

The green lines represent the generated plain knit, whereas the purple shows the spline that has been extracted from 232

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the knit’s polyline vertices. In this model the spline was extruded with the known ratio of diameter and cell height and did not produce any intersections90 in its course, except in the edge surface areas where cellular height was diminished. Future tests should therefore locate the critical areas and calibrate the tubular diameters or overall scale accordingly.

Ill. 133 Digital model of plain knit with cellular deformation

The relationship between tubular dimensions and minimum fabrication dimensions represents a known constraint since a minimum radius is needed to allow facile removal of support structure material. This radius must be negotiated with the setting for cellular resolution and the choice of applied additive fabrication. The digital model created here was additively fabricated with a light-hardening polymer printing process using a white, semi-rigid material.91 Analogous to the previous test, in the executed model the structural continuity remains intact even under local cellular deformations. This aspect shows that the assigned movement ranges function in accordance with the knitting protocol.

90 91

Intersections were checked digitally within Rhino3D. The overall dimensions of the print sample were 299.64 x 214.69 x 108.21[mm].

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Ill. 134 Top right: additive fabrication of knitted geometry, top left: model with support structure, bottom: cellular variation of the plain stitch

The overall tubular diameter sizing of the sample92 led to geometric intersections in large areas of the model that prevented any examination of potential flexibility and material engagement. The model nevertheless demonstrated the desired irregularities in the knit’s course caused by the calibration of local deformation values. The experiment achieved a correlation of the yarn’s surplus length, created by a computational definition of cellular heights that specified graded, locally expressed movement in the digital yarn’s performance, further amplifying the distinct presence of the cellular morphology. The implementation of a single form-defining numerical input source for the calibration of two separate levels of geometric definitions contributes to a conceptual design process in which abstract relationships articulate a final morphology that can hardly be pre-conceived as such.

92

The chosen piping diameter is 2 mm.

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Experiment Step 6: Spatial adaptation of multiple knits to a planar and spatially complex geometry with local deformation values in a patterning sequence retrieved from an image source and CA The final experiment expands this concept further to integrate a third level of form definition instance by extracting the patterning information from a single numerical matrix. This step blends cellular and local deformations with material presence (through a specific pattern) by cross-referencing a single input source. This multi-level engagement of external drivers on a parametrical matrix driving a CAD model represents a highly abstracted interface for design activity. Such an implementation of a single input that can be harvested from the known sources on different hierarchical levels produces informational overlaps and geometric amplifications that exceed straightforward preconception but can be detected nevertheless. The subtle blend created by this interwoven process goes beyond conventional mechanical structural adaptation of a single component property, affecting the definition of the overall geometry and its local segments simultaneously.

In the following test a choice of additional knitting patterns has be encoded that alter the performance of the structural assembly and define93 material presence or absence to allow a further mechanical control of the designed structures. Pattern variation requires the control of the individual cell’s space with varying cellular neighbourhoods to ensure that the course of the thread passes continuously through the textile object. The experiment tests these pattern clusters with a flat matrix and a spatial one.

Encoding various knitting situations The diagram shown below (Ill. 135) displays a selection of possible knitting situations that structure the material presence within the cellular matrix and lead to varying densities and thus trigger differing mechanical performances of the structured assembly. The pattern-specific encoding defined alternating vector courses that were based on the first three plain knit components (Ill. 137).

To express the individual stitch course, an abstracted graphical encoding of each individual situation was developed, using a textual codification that allowed better readability as well as an easier addition, subtraction or overall alteration of the initial plain knit components (described as M1, M2 and M3) (see Ill. 136). The encoding pattern included the component number and the utilisation of the initial plain knit elements, as well as identifying additional lines that had to be added or subtracted from other cellular components.

Ill. 133 COMP16 [component number] MAIN (M2) [component 2 of the plain stitch) + lnH3 [horizontal thread 1] + lnH4 [horizontal thread 2]

It is obvious that the components presented here define only a selection of the manifold knitting situations imaginable. Since the experiment is not designed to deliver a comprehensive modelling of this aspect, but focuses on investigating a new geometric and material interaction, the aspect of lexical completeness was neglected.

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Individually defined cells (Ill. 136) were grouped into coherent pattern clusters to grant control over the threads’ spatial continuity. These pattern clusters (Ill. 137), which describe, for example, distinct edge conditions, are geometrically interdependent and had to be transferred in sets to the spreadsheet that controls the cellular distribution sequence.

Ill. 135 Selection of encoded knitting components and numerical patterning

Through the implementation of pattern sequencing, now it was possible to introduce another parameter—besides the control of surplus length and cellular deformation values—to control morphology and movement potential in a novel fashion.

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Ill. 136 Graphical encoding of knit cells with descriptive nomenclature of thread structure

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Ill. 137 Cellular clusters or interdependent knit configurations

After the initial components were encoded, a test was conducted on a simple point grid that included the variety of components (patterns) identified in the overview diagram. This test used an image converted into a binary matrix through the known processes to test whether the assigned scaling ranges were functioning and structural coherency was achieved. The test also investigated the transferability and effect of the pictorial source for the control of movement on a cellular basis.

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Ill. 138 Left: overlay of image source and knit pattern, right: demonstrator patch with local gradient deformation of the computed polylines

The preliminary experiment yielded two findings: •

The structural continuity of all the employed cellular patterns was maintained94 and the knitting logic respected.

•

The local alteration of the cell-specific behaviour was also observed in the overlay between the driving image source and created geometry.

The final test applied the external numerical spreadsheet data on three interdependent hierarchical levels (Ill. 139) of the overall morphology.

Level 1: Pattern definition – The input information, in this case a binary CA pattern from the previous experiment, was used to define the presence or absence of knit cells by scaling the spreadsheet data into a binary matrix (“2”-knit, “1”-no knit). From this initial layout the pattern clusters were extracted to ensure the linear continuity of the thread throughout the textile.

Level 2: General definition of surplus length – The CA pattern was employed to calibrate of yarn’s surplus length, by varying the offset heights of the initial cellular definition. The binary CA data set was differentiated by a third number (“3”) reserved for the internal cells within the pattern perimeter of the area defined by Level 1.

Level 3: Local deformation on a cellular level – The last step alters the movement of the yarn’s course by steering the change in the coordinate parameters that can be addressed specifically.

After the individual lines were computed they were joined and resolved into a single polyline. From this object a curve was generated through the polyline vertices.

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Ill. 139 Data-scaling on three hierarchically interconnected levels

The application of the cellular component distribution yielded the following pattern (Ill. 140). The patterning sequence traced the created perimeter of the CA and delivered variation in the internal areas of the knit. Increased surplus length and local deformations were identifiable in the respective areas. The matrix applied on the cellular level produced observable graded irregularities in the knit’s course.

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Ill. 140 Created knitted structure with implemented levels of CA-based information. Red areas show pattern change.

The set of geometric dependencies developed here is not based on the definition of distinct local spatial conditions, but can be applied to multiple-base surfaces if their binary resolution complies with the matrix values. Such created assemblies can therefore be stored and effortlessly applied to multiple spatial situations. For this purpose the previous parametric model was transferred to the more complex root surface shown below (Ill. 141). The design activity that takes place in such a process concentrates on defining the relational geometric dependencies that can be adapted to boundary geometries in varying scales, and identifies domains with specific mechanical characteristics that are actualised in scale in the later physical model.

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Ill. 141 Re-application of the patterning, cellular height and local deformation ratio on an alternative cellular matrix

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Excursus: Design and additive fabrication of a knitted structure with the D-shape process The previous experiments focussed on the idea of a dynamic material performance of additively fabricated samples that could be triggered by a controlled knitting logic. The conducted tests unveiled and discussed the still persistent geometric and fabrication constraints that hinder a straightforward realisation of additive fabrication for full-scale dynamic building components with regard to material qualities and scale. The excursus presented here investigates an application of the previously developed morphologies for an additively fabricated compressive structure that operates under different boundary conditions of scale and stability.

The experiment researches a structure of textile tectonics that shows load-bearing capabilities for stress forces in building scale. Local irregularities of its discrete members—present in the digital model—can be transferred and so shape an irregular three-dimensional morphology that is hard to create in a conventional manufacturing process. The sample presented here represents a first test of whether developed geometric and design parameters can be transferred equally to different scales and is geared mainly to examine the geometric boundary conditions that can be realized by such an approach.

In order to create a printable artefact, the research extracted (Ill. 142) an area of the final knitted design from Experiment 6 and tested the fabrication of such with the previously mentioned D-shape process. The selected area was scaled to occupy a spatial extension of 0.60 m x 0.80 m x 1.40 m. The overall weight of the sample was 135 Kg.

Ill. 142: Right: piped segment, left: digital model of the extracted area from the final model

In the following step constraints of the additive fabrication technology had to be applied in correspondence to the overall morphology of the piece. Since few data have been collected on the stability of structures created this way, the minimum thread thickness in the test was increased to 5 cm, adding 1 cm to the achievable minimum of 4 cm for additional stiffness. To create a watertight mesh of the many intersecting tubular elements, the Uformia plug-in (Uformia AS 2011) for Rhino was used, which is based on an algorithm for the volumetric description of novel solid 243

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geometries by Fryazinov et al. from 2011. A first inspection of the sample suggested that these densely packed structures can be potentially thinned significantly since many of the threads intersected, strengthening the component’s stability and thus producing enhanced translucency and better readability of the knitting logic. The dimensioning of these elements therefore depends on the spatial packing and the main force flows that have to be brought in correspondence with the build direction.

Ill. 143 Left: knitted wall segment, right: detail with cavity

The test showed that fabrication of such structures can be achieved and deliver results in robust quality. The developed digital workflows that defined topologically invariant cellular elements could be readily implemented and scaled to the appropriate dimensions of the later piece. Local calibration of the structural behaviour of these building elements could in the future be achieved via processes to optimise form and topology and drive a structural reaction of the morphology through tighter cellular distribution or increased tubular thickness. Future research must investigate spatial concepts that can be realised by such approaches that exceed the scale of the sample presented here. The high dead loads of building elements created this way requires investigations on appropriate design processes to integrate fabrication constraints, local inspection of geometric morphology and structural dimensioning.

The main load-bearing capabilities of layered assemblies with natural stone granulate are based on compressive loads and require the development of engineering solutions for bearing tensile forces to allow a broader spectrum of building applications. To date little is known about potential internal structural reinforcements that could be feasible for certain geometries. First studies have been submitted by James Gardiner/Faan Studio on using the D-shape process to fabricate building elements that contain cavities to house traction rods, but so far no full-scale tests have been completed.

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Ill. 144 Cavities for tensile rods in printed column component (design by James Gardiner/Faan Studio)

The free control over the structural geometries allows a re-evaluation of classical construction elements like beams, ceilings and walls, which are usually defined by a given construction sequence of standardised building elements.

Ceiling elements that contain flush beam strips or ceiling joists can be integrated into a complex assembly of threedimensional morphologies and have their dimensioning adapted to local geometries if solutions for bearing tensile forces can be developed (Gardiner 2009). These structures would combine structural performance with a novel tectonics that is local, variant and multi-functional. The moderate building costs for the samples produced favours an application in architectural projects, yet further research must be performed on the mechanical properties of additively fabricated structures and their long-term performance under constant and varying loads. Existing knowledge on the structural performance is sparse and does not cover anisotropic behaviour, information on the curing time of the printed material, or its performance in interior and exterior environments.

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5.3.5 Conclusion The series of experiments presented here demonstrated a design process that followed a knitting and weaving structural logic to create complex morphologies with computationally based mechanical properties driven by intertwining different formgiving parameters on many hierarchical levels. The conceptualisation of the digital model implemented a future material performance through computational control over a yarn’s surplus length, patterning methods and local calibration of spatial thread behaviour. This aspect was further enhanced by local material variation achieved with contemporary multi-material additive fabrication processes or through the appropriate dimensioning of structural elements. The text gave practical boundary conditions for modelling such structures to provide for damage control under additive fabrication constraints and pointed to the structural differences from classic woven or knitted textiles that have to be considered.

The envisioned dynamic properties of additively fabricated designs suffered from the available fabrication scale and from material quality issues. Existing polymer-based additive fabrication apparatus allows only the creation of samples too small to provide for free structural movement. Material brittleness, deterioration over time and environmentally hazardous print materials affect their usability for architectural purposes. The materials employed in polymeric print processes represent a problematic obstacle for wider applications in an architectural context since these quality issues appear unlikely to be overcome soon.

The presented test that used resin bound natural stone granulates for a full-scale component with a knitted structure promotes a design approach in which additive fabrication tectonics can be utilised for a geometrically expanded architectural language that projects geometric morphologies inherited from other material systems to new building structures. The geometric tectonics of knitting, known from our everyday experience with textile products, can be transferred to an unexpected context and building scale. Those geometric intersections of the linear elements that were problematic for flexible assemblies in this case granted additional stiffness and improved the load-bearing capabilities of the structure. The observable permeability of additively fabricated textile tectonics allows control over translucency and diffuse spatial differentiation and can be coupled with the structural dimensioning of individual threads retrieved from optimisation processes to augment the functionality of such elements.

The research tried to show that the openness of the employed interface and formgiving entities give great latitude for artistic and architectural design since translations, interconnections and re-applications of the employed formgiving factors are facilitated. This process, representing a major departure from the Euclidian geometric protocol, blends different hierarchical levels into an interconnected tissue of computational, mathematical and artistic origin with different design interfaces. The emerging complexity that can be observed expands fully pre-conceivable, pragmatic and rational materialisations of earlier eras and fosters geometric and numerical overlaps that come with their own formal language and a new aesthetic of local irregularity and connectivity apparent between the different levels of formation that would have to be chosen depending on the design task and location. As stated repeatedly during the text, this experiment was not to be regarded as a complete digital knitting system, as this would require a different research approach and thematic delineation, but as an investigation into a processural composite of tuneable formal and material reactivity and great openness, developed in correspondence with a distinct tectonics derived from additive fabrication.

The break in structural regularity achieved through subtle alterations of a discrete element’s spatial course, observable in all of the experiments in this chapter, fosters a different perception of tectonics created this way when applied to building scale. The constructive order that can be traced in the buildings of Modernism separated building elements by their hierarchical load-bearing functions and demonstrated rationality and dimensions that often overwhelmed the 246

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human scale. The modulation of morphologically differentiated members for a shared structural goal, by contrast, introduces a scale shift and assigns value to locality and individual difference, promoting a perception of such building tectonics in a less hierarchical and straightforward manner. Building elements defined this way could contain segments with varying structural roles that are subtly integrated into the assemblyof the whole. Such complex tectonics can, on the one hand, be transferred to more classic building elements like walls, roofs and columns, but on the other, can also initiate a new and unprecedented typology of architectural components. The given example of the vaulted structure in which a solid column transcends into an open gridshell can be seen in this context. These elements avail themselves in a distinct manner of the properties of additive fabrication and can provide unprecedented morphological results.

The mentioned overlaps of interacting information acting on the final design can grant a locus for an intentional, digitally defined opaqueness between cause and action that is nonetheless far from arbitrary. Accepting that design processes conducted in this way entail a perceptible creative imbalance between formgiving input and morphological output opens the door for a new artistic and architectural design process that utilises computational intelligence in a novel manner. Similar to the painter who blends, smears and layers colours without meticulously controlling and planning the result, so can we enter into a practice that provides areas of control and zones of free action. This eclectic blend of interacting functions, information and actions can hereby introduce an architectural practice that is surprising, sensitive and human. The willingness to engage with a design process under these circumstances can support a new stream of architectural designs in which rationality, richness of form and new artistic and conceptual workflows can be realised.

In this it would be similar to the individual research approaches practiced by Desargues and de L`Orme in the design of the distinct trompes, yielding an architectural practice that avails itself of the new formal and fabrication options shaped by the personal ideas of the authors but transcends them to produce individualised architectural results. The different floral edge-lines of the respective trompes materialised the projective geometry protocol developed in keeping with the architect’s individual and momentarily abstract understanding of formgiving. The text attempted to sketch the conceptual backgrounds of the individual designs through a broader look at the context of each individual’s work and found arguments that—in Desargues’ case—promoted a strengthening of the methodological and mathematical aspects within architecture, or—in de l`Orme’s view—utilised the new geometric techniques to create new formal freedom that could help to approximate nature’s richness and architectural formgiving. Following Toni Kotnik’s95,

96

viewpoint, which sees geometry within an architectural context as an attempt to visualise a

“mental picture” emerging from a cultural understanding of form and its derived symbolism, further discussion is required of the conceptual aspects that can arise out of this computational experiment through future studies on an architectural scale.

For further reading see “Experiment as Design Method. Integrating the Methodology of the Natural Sciences in Architecture” (Kotnik 2011). The author delicately outlines the conceptual, scientific and experimental boundary conditions that acted upon historical research strategies in natural sciences like mechanical engineering, transcending them to produce strengthened applications in structural engineering and later architecture. The author offers a reasonable differentiation between the architectural and structural engineering design strategies and the role of the experiment associated with such strategies in the different disciplines.

96 Kotnik outlines this aspect on the example of geometry in an architectural context: “Traditionally, the role of geometry within the design process is, in this respect, understood as the rational foundation of architectural thinking, on a constructive and perceptual basis as well as on a conceptual one. […] But the use of mathematics within architectural design is not, like with Galilei, motivated by a will to describe physical reality that can be experienced but is, above all, a means of representing a mental picture.” (Kotnik 2011, 37) 247 95

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Conclusion and Outlook

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6.1 Summary The conducted experiments proved that computational tools can be employed to create a new type of additively fabricated materials with structural and material differentiation and controllable performance. The first two experiments investigated such performance differentiation through calibrated morphologies within a single material and through volumetric composites that used contemporary polymer-based multi-material additive fabrication technologies. The research showed that structural analysis software could be used to drive the goal-oriented calibration of heterogeneous material composition. The digital cellular components developed to construct auxetic and textile structures allowed the geometries to be tuned to optimise a specific, goal-based material performance and proved applicable over different scales. The different geometric toolsets were also applied in a demonstration that employed the recently developed D-shape process to transfer a macro-scalar knitted structure directly to a life-size building scale.

The last experiment showed that through such new digitally driven processes an architectural practice can emerge that embraces geometric freedom, formal variation and structural performance for complex material morphologies— yet fabrication constraints remain. The additive fabrication processes employed here were based mainly on polymeric materials that suffered from mechanical deficits that render the quality of additively fabricated artefacts inferior to products made by classical industrial fabrication technologies like injection moulding or extrusion casting. The anisotropic properties that derive from the vertically layered deposition of material weaken all additively fabricated structures orthogonally to the build axis, posing significant mechanical deficits that are hard to overcome. The postcuring process of Polyjet parts emits harmful chemicals that are not biodegradable and cannot be recycled or reused.

It is questionable whether these polymer-based processes can be applied effectively in the building sector since longterm stability and functionalities are required that have yet to be achieved. Despite a drop in the costs of acquisition and production of additively fabricated components in recent years, the general price level for such artefacts is not competitive in the construction market. Future research should develop computational tools for a comparative analysis of conventional and additively fabricated components to offer more transparency about the true costs of manufacturing and thus encourage the technology’s propagation.

For an architectural application of additively fabricated components, fabrication processes with larger build sizes, greater precision, higher speeds and increased layer thicknesses have to be developed that allow manufacturing in building scales. The existing research on large-scale additive fabrication by Khoshnevis and the Concrete Printing group at Lorborough University points in this direction, yet the process’ inherent lack of a support structure to create overhanging geometries does not allow utilisation of the full geometric freedom usually associated with additive fabrication. Enrico Dini’s D-shape process provides this stabilising material during the printing process, yet requires further development to surmount the mechanical challenges presented by the build materials. For application on a building scale a new typology of architectural components has to be investigated and developed, which takes advantage of the generic manufacturing tectonics of additive fabrication to achieve geometric composition. Variations of print materials for architectural applications have to be further expanded. The current state of technology favours structures with compressive load-bearing facilities in building scale, since, as discussed above, the properties and scales of purely polymer-based processes do not promote tensile structures.

Two of the experiments conducted were affected in their functionality by the relationship between minimum material dimensions and overall printing size. In the case of the knitting experiment, the cellular components suffered from geometric intersections that prevented free movement and changes in form. The auxetic tests showed lower reactivity in their mechanical performance due to the minimum dimensions required for the ligaments in 1D 249

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and 2D lattice structures, or because of geometric intersections that constrained cellular behaviour in the 3D auxetic knots. These constraints could be overcome with larger printing dimensions that will potentially emerge in the future.

The methodological approach practiced, which interconnected different fields of scientific research, contributed successfully to the set-up of the experiments. Existing research approaches on the fabrication of functionally graded and auxetic materials informed the experimental approach effectively; textile assemblies like weaving and knitting were suited for cellular geometry description and helped to illustrate a different formal conception of integrated dynamic movement and local geometric control under the additive fabrication tolerances. The conceptual implications of a workflow interweaving digital design, additive manufacturing and material performance could be investigated with the technologies available. The geometric control over many different kinds of structural assemblies proved achievable and could, in principle, be transferred to physical artefacts. The design approach focused on the definition of intensive material properties, which could be encoded into cellular components and clusters of such, appeared suitable for adaptation to improving technologies and scales. The methodological approach established constructive parallels between contemporary technology developments against the background of the generation of historical architectural knowledge, in this case the reception of projective geometry in architectural formgiving that had synchronised representation, the process of drawing and fabrication in a single format. This new realm of conceptual formgiving has not yet been fully exploited on a building scale and requires improved fabrication technology and further study.

The research showed that a different conception of material that is variable and configured by locality and desired performance can be achieved through layered manufacturing. This aspect, which breaks with the traditional view within architecture on the relationship between material, structure and form, constitutes one of the key contributions of this thesis. Components that are characterised by unique and local materiality and structural composition can be further enhanced by form- and shape-optimising procedures that were not investigated here. Such components or building elements in building scale would allow a unique formal and tectonic architectural language to emerge, in which artistic and performative aspects could be integrated and fabricated in an intertwined process. The experiment that created a heterogeneous material performance by calibrating the structural composition within a single material bears potential for transfer to such large-scale printing processes and appears suited for research that follows up on this thesis. It has been shown in experiments conducted by the author and others that mechanical calibration can be achieved by controlling the bulk density of a material, which can be achieved through integrated cavities and computationally defined porosity. This approach that was initially geared towards design processes for dynamic material behaviour can be transferred to research on the creation of compressive load-bearing structures. Future experimentation with textile-inspired structures of great irregularity could be coupled with integrated load-bearing functionalities realised through the appropriate dimensioning or density of the individual linear threads, which then could be applied to classical architectural building elements like walls, beams or columns, but solutions are required to transfer the load of strain forces. Print materials that are packed with additional structural fibres similar to the UHSFC (Ultra High Performance Fiber Concrete) (Bechtold 2008, 162-165) appear to be a first step in this direction. The combination of compressive load-bearing elements with external tensile members has been already attempted but needs further examination before it can become a feasible approach to grant broader structural performance and a wider scope of architectural applications to additively fabricated building elements.

The virtues of mass customisation that can be realised through computational design and additive fabrication can facilitate the development of load-bearing structures and novel spatial concepts that introduce morphological 250

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variation and human scale into building components. The potential implementation of multiple building functions into a single building component, as outlined by this research, can hereby potentially avail itself of scientific knowledge from biology and botany to create heterogeneous materials with structural hierarchy. The research pointed to recent developments in which additive fabrication was coupled with related technologies to create complex components with multiple embedded functionalities. Such developments can enrich this approach further and constitute their own area for future research.

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6.2 Recommendations Future digital design processes that integrate additive manufacturing processes require several technological improvements. Volumetric descriptions based on a geometrical mesh have to be replaced, ideally by file formats that provide fabrication information directly. The recently introduced *.amf file (ATSM 2011) format, which integrates graded material descriptions and multi-material printing options, expands the limitations of the *.stl format used in the last decades and represents a first step in the right direction. Yet the format is still based on a meshed geometry that must be abandoned if structural differentiation and detail are to be applied on a building scale. Feature-based volumetric descriptions developed by Fryazinov et al. (2011) appear to offer an interesting path in this direction. This novel volumetric geometry definition includes the extraction of vertical deposition information with respect to the printing resolution without the necessity of creating watertight meshes. These developments can create larger and more complex modelling assemblies, allowing multiple blending and Boolean operations that normally present problems when the number of geometries involved reaches a critical mass. To achieve progress in the calibration of micro, meso and mega-structures in building dimensions these geometric processes have to be further developed to allow their effective implementation in future architectural workflows. Future research is needed to develop computational tools that allow a feasible definition of multi-material composites and then team them with structural simulation with respect to anistropic material properties. These can then, in turn, inform structural dimensions and manufacturing build directions. Coming research should investigate joint assembly systems for micro, meso and macro-scalar additively fabricated components. The creation of complex components that avail themselves of the benefits of additive fabrication from the nano-scale upward can open up an unprecedented branch of materials with combined structural, electro-chemical, logistic and mechanical functionalities. Multi-layered performances that are conventionally realised through assembly systems of discrete mechanical components can then be achieved by calibrating material and structural composition to yield more integrated and bespoke building components.

Future research should further explore fabrication methods with more environmentally friendly materials that produce artefacts with longer sustainable lifetimes to allow broader implementation in architectural production. Fully recyclable multi-material printing, as sketched in a paper by Hiller and Lipson, offer a valuable starting point for such research (Hiller and Lipson 2009). Existing research on chemically enhanced resins as presented by Kumar and Kruth (2009), which adds enhanced functionailties to additively fabricated components by controlling mechanical and performative properties chemically, appears to be an interesting path worth pursuing.

An application of additive fabrication in an architectural context relies on properties that render the technology in a different way from existing manufacturing methods, and which can enrich future architectural designs. This aspect was highlighted specifically by Bourell, Ming and Rosen in 2009 and needs to be practiced through education, research and industrial projects. The growing number of rapid prototyping models to visualise complex architectural geometries trains an understanding of these properties in practice and academic education (M. Burry 2003) and has to be transferred to full-scale rapid manufacturing, with a focus on the innovative constructive conditions it enables.

Building tolerances, structural behaviour, construction sequencing and novel assembly sytems of such architectural elements present a broad, largely unexplored field for future research. This novel building tectonics enriches a historically persistent architectural discussion on structure, form and material performance under the altered boundary conditions that were presented here. The historical analogies outlined by this research should be understood in that sense.

These novel digital design processes come with a set of unique interfaces that exert their impact on the final architectural structure. The persistent gap between the visualisation and fabrication of architectural designs that 252

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accompanied the practice over centuries has been closed through a direct retrival of manufacturing information from the created model. This development that was already observed—in a constrained fashion—in subtractive manufacturing processes unfurls completely here, demanding better understanding and further practice. Once fabrication dimensions increase, dynamic changes in the form of additively fabricated tectonics can be studied better than at present.

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6.3 Final Reflections The coming years will surely see proliferation of the different technologies described here; thus relevant research areas that can be beneficial to investigate have been outlined throughout the text. Many of the processes described still suffer from technical problems or lack the financial means to lift the technology to a higher standard, yet the significance of these developments for a novel approach towards architectural formgiving can be already traced today.

The level of abstraction introduced by the new design processes provides great openness for the implementation of formgiving drivers from a variety of sources. Contemplating these design-relevant players represents a different process of architectural form-finding that can open up a space of geometric and tectonic flexibility and provide a locus for a new architecture of individual scale and essentially humanistic variance.

Architectural design processes amalgamate functional, structural, emotional and economical requirements in a nonlinear fashion. The emotional experience of great architecture is often driven by the viewer’s understanding—or notion of comprehension—that a creative work has been achieved which subtly complements the pragmatic requirements of program and structure with an artistic expression that goes beyond the object itself but physically testifies to the genius loci, its position on an historical and a theoretical timeline, and an experience of the architect’s approach to human interaction.

The emergence of exceptional artistic creations requires a practice beyond the skilful eloquence of technology but should allow the sensuous expression of the creator’s individuality, directing his conscious and unconscious creative abilities toward the design challenge (Senett 2008, 73 ff.). This essentially personal practice leads from the common to the distinct and can be traced in the masterpieces of the traditional crafts whose excellence evades a reductionist explanatory model.

The idea of “craft” that recently appeared in digital architecture suggests that a comparable processural eloquence has been achieved, through which information and practice can be transformed into tacit knowledge to shape a unique artefact. The ongoing general contemplation on the functionality and applicability of constantly changing digital tools, on the other hand, relativises this confidence. It is a legitimate question as to whether we have already transcended the everyday routines of our tools, or are still in a process of analysing their consequences for architecture. The future quest for the artistic evolution of our discipline must lie in identifying the locations where a shift from tooling to crafting might be achievable under the above conditions, from which a new generation of pioneering architecture can arise.

The ability to synchronise human imagination and realisation in a material world driven by an integration of design and manufacturing into a joint process can thus establish a platform on which the qualities of architecture will be negotiated in a radically different manner.

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Illustrations and Tables Ill. 1 Left: contour crafting of a barrel vault, right: adobe masonry distribution of bricks (Khoshnevis 2004, 9) ......... 35 Ill. 2 Building component fabricated by the Concrete Printing Group at Lorborough University (arbitare 2010) ....... 36 Ill. 3 Left: “Parametric column 1” (Gardiner 2009), right: sections of printed with D-shape technology ..................... 37 Ill. 4 Left: digital model of a vaulted structure, right: materialised D-shape model ............................................................. 40 Ill. 5 Left: D-shape print of vaulted structure before depowdering, right: top detail .......................................................... 40 Ill. 6 A simple catastrophe: A sudden change in potential energy (illustration from Woodcock and Davis 1978, 48) . 61 Ill. 7 Kelvin structure (Kelvin 1887)............................................................................................................................................. 69 Ill. 8 Mechanism (a) and structure (b) in Deshpande, Ashby and Fleck (2001) ................................................................... 69 Ill. 9 Left: Poisson ratio with positive value, right: Poisson ratio with negative value ........................................................ 70 Ill. 10 Auxetic materials in different scales (Alderson 1999, 385) ........................................................................................... 72 Ill. 11 Left: non-auxetic material performance, right: lateral expansion in an auxetic cell (Alderson 2005, 14) ............. 73 Ill. 12 Sub-unit of theoretical auxetic molecular network: “(1,4)-reflexyne”. (Alderson, Daviesy et al. 2005, 34) ......... 74 Ill. 13 Left: SLM sample of auxetics (Rehme and Emmelmann 2009), right: auxetic knit by (Ugbolue et al. 2008) ..... 74 Ill. 14 Left: Different Poisson ratio cells (Bubert et al. 2008, 5), right: morphing wing components ............................. 76 Ill. 15 Chiral auxetic cell (Prall and Lakes 1996, 8) .................................................................................................................... 78 Ill. 16 CHISAMCOMP panel developed by the University of Catani, Italy (Meli et al. 2009) .......................................... 79 Ill. 17 Auxetic behaviour of rotating squares (Grima and Evans 2000, 1563)...................................................................... 80 Ill. 18 Right: open-cell polymer foam, left: re-entrant foam with a Poisson ratio of -0.6 (R. S. Lakes 1987, 1039) ...... 81 Ill. 19 Left: idealised re-entrant unit cell (R. S. Lakes 1987, 1039), right: knot in (Friis, Lakes and Park 1988, 7) ......... 82 Ill. 20 Magnox reactor with three-dimensional auxetic structural composition (Alderson 1999, 385)............................. 83 Ill. 21 Hexagonal lattice cells with curved bi-material ribs (R. Lakes 2007) .......................................................................... 84 Ill. 22 Hierarchically graded structure of bamboo (Amada, Fukao and Yuntao 2000, 058)............................................... 88 Ill. 23 Fibrous, laminar particulate and porous structures in compact human bone (R. Lakes 1993, 514) ..................... 88 Ill. 24 Rapid manufacturing of carbon nanotube composite structures (Brice and Herman 2005) .................................. 90 Ill. 25 Shape-deposition modelling of “Sprawlita”, a dynamically-stable running hexapod (Cham et al. 2002, 2)........ 90 Ill. 26 Gradient coating of copper /nickel alloys in a rocket combustion chamber (Holmes and Mc Kechnie 2001).. 92 Ill. 27 Manufacturing principles of functionally graded materials (Myamoto et al. 1999, 163).......................................... 93 Ill. 28 Graded distribution of materials with the LENS process (Liu and DuPont 2003).................................................. 95 Ill. 29 Insole construction with air-pockets (Rudy 1977, 1) ..................................................................................................... 96 Ill. 30 Calibration of cellular tube geometry................................................................................................................................ 97 Ill. 31 CAD model of tubular structure and Zcorp plaster print ............................................................................................ 98 Ill. 32 Additively fabricated base materials under 15N force (Bickel et al. 2010)................................................................. 98 Ill. 33 Deployable wing (Maheshwaraa, Seepersad and Bourell 2007, 10,11) ....................................................................... 99 Ill. 34- A skull model made of two materials (Gibson, Rosen and Stucker 2010, 425).....................................................100 Ill. 35 Hydrogel print with multiple stiffnesses (Mookerjee et al. 2009, 7)..........................................................................101 Ill. 36 Left: Voronoi pattern (N. Oxman 2010, 81), right: 1:3 prototype (N. Oxman 2010, 79-80) ...............................102 Ill. 37 Top: measurement of scattering profile, bottom: measurement of reflection profile (Milos et al. 2010, 2) ......103 Ill. 38 Additively fabricated marble with sub-surface scattering optimisation (Milos et al. 2010, 10) ............................104 268

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Ill. 39 Left: variant approach, right: generative approach (Bhashyam, Shin and Debashish 2000, 122, 121) ...............106 Ill. 40 Graded space-grid structure (Hanna and Mahdavi 2005, 78).....................................................................................107 Ill. 41 Left: Connex material properties, right: distribution under vertical load (Hiller and Lipson 2009, 4,6) ............109 Ill. 42 Process (from left): Material distribution, graphical display, mesh geometry (Shin and Lee 2006, 665-666) ....109 Ill. 43 Material properties with differentiated properties in simulation and physical tests (Bickel et al. 2010, 6) .........110 Ill. 44 The Lamentation over the dead Christ c. 1490 (Andrea Mantenga) on display at Pinacoteca di Brera, Milan .115 Ill. 45 “Les Perspecteurs” by Abraham Bosse (1647) .............................................................................................................117 Ill. 46 Construction of the trait for the trompe d´Adnet in Trevisan (1999, 1)..................................................................118 Ill. 47 Trompes by Desargues (left) (Desargues and Bosse 1653, p79), de l`Orme (right) (de L´Orme 1567, 196) ....120 Ill. 48 Left: cupola of S. Sindone, right: projective construction of the cupola’s windows and ribs ..............................121 Ill. 49 Comparison between trait and digital material model .................................................................................................124 Ill. 50 Poisson value alterations under continuous lateral stress............................................................................................133 Ill. 51 Testing gauge by Rehme and Emmelmann (2009, 131-132) ......................................................................................134 Ill. 52 Top: initial testing apparatus for strain forces, bottom: testing apparatus for stress forces .................................135 Ill. 53 Revised version of the strain gauge .................................................................................................................................135 Ill. 54 Encoded transformation of the re-entrant ligament with a Poisson ratio of zero .................................................136 Ill. 55 Top: design of the cellular element, bottom: geometric set-up of the test specimen ............................................137 Ill. 56 Implementation of the physical test sample ..................................................................................................................138 Ill. 57 Extension diagram of re-entrant ligaments....................................................................................................................139 Ill. 58 Connex print of 1D graded auxetic knot structure ......................................................................................................140 Ill. 59 1D auxetic structure—left: unstressed, right: stressed.................................................................................................141 Ill. 60 Bending performance of the honeycomb ......................................................................................................................143 Ill. 61 1D auxetic cell, load case: stress ......................................................................................................................................145 Ill. 62 1D auxetic cell, load case: strain ......................................................................................................................................146 Ill. 63 Geometric control of re-entrant cellular behaviour with an array of bow-tie-shaped elements ..........................147 Ill. 64 Top: topological design of the cellular element, bottom: geometric setup of the test specimen.........................148 Ill. 65 Lateral bending behaviour of 2D auxetic panels through edge unilateral vertical constraints .............................149 Ill. 66 Graded distribution of bi-axial auxetic behaviour ........................................................................................................150 Ill. 67 Connex print of 2D graded auxetic knot structure ......................................................................................................152 Ill. 68 2D auxetic structure—left: unstressed, right: stressed.................................................................................................153 Ill. 69 Re-entrant cellular behaviour under compression load—left: flat, right: unflattened............................................154 Ill. 70 Circular gradients of re-entrant behaviour expressed in a two-dimensional matrix...............................................155 Ill. 71 2D auxetic cell, load case: stress ......................................................................................................................................157 Ill. 72 2D auxetic cell, load case: strain ......................................................................................................................................158 Ill. 73 Unit cell of re-entrant foam—illustration taken from E. A. Friis (1988, 7).............................................................160 Ill. 74 Parametrisation of Friis and Lakes’ auxetic knot element...........................................................................................161 Ill. 75 Plaster-printed model of graded 3D auxetic knot structure .......................................................................................162 Ill. 76 Idealised 3D auxetic cell (R. S. Lakes 1987) ..................................................................................................................163 Ill. 77 Encoding of the idealised unit by R. Lakes ...................................................................................................................164 Ill. 78 Catenoid-helicoid surface with a periodic tiling of maximum-re-entrant 3D auxetic knots .................................165 Ill. 79 Single row of auxetic cubic elements with gradual distribution of re-entrant values .............................................166 Ill. 80 Implementation of the specimen.....................................................................................................................................166 269

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Ill. 81 Printed model before removal of the support structure .............................................................................................167 Ill. 82 Graded distribution of tri-axial auxetic behaviour........................................................................................................168 Ill. 83 Connex print of 3D graded auxetic knot structure ......................................................................................................169 Ill. 84 3D auxetic structure—left: unstressed, right: stressed.................................................................................................170 Ill. 85 3D auxetic structure with gradual degrees of lateral expansion .................................................................................171 Ill. 86 3D auxetic cell, load case: stress ......................................................................................................................................173 Ill. 87 1D auxetic cell, load case: strain ......................................................................................................................................174 Ill. 88 Left: material differentiation, right: structural differentiation ....................................................................................177 Ill. 89 Left: material distribution right: combustion chamber coating by (Holmes and Mc Kechnie 2001, 2) .............180 Ill. 90 Material composite with truncated octahedral and cubical elements ........................................................................180 Ill. 91 Left: material distribution within matrix material, right: peak loads in cubical geometry .....................................181 Ill. 92 Topology optimisation of constrained force flow within abstracted design space ................................................182 Ill. 93 Implementation of the FE model....................................................................................................................................185 Ill. 94 Extraction of vertical displacement information for definition of composition control ......................................186 Ill. 95 FE-based material distribution.........................................................................................................................................186 Ill. 96 Physical properties of the print material (VeroWhite-TangoBlack) ..........................................................................188 Ill. 97 Experimental set-up for collection of stiffness values.................................................................................................189 Ill. 98 Distribution of the stiffness values and assigned vertical forces ...............................................................................190 Ill. 99 Left: CT with a line detector, right: area detector (Bundesanstalt für Materialforschung 2006, 2) .....................191 Ill. 100 Left: CT image of vertical section through specimen, right: set-up of the radiological screening ....................192 Ill. 101 Left: material distribution within a yarn, (right) additively fabricated yarn geometry ..........................................198 Ill. 102 Relationship between cellular size and tube diameter................................................................................................199 Ill. 103 Peirce’s model for plain woven fabric (Chen 2010) ...................................................................................................199 Ill. 104 Vectors and coordinates for tunable encoding of line elements..............................................................................201 Ill. 105 Left: Kilim weaving pattern, right: patterning with warp and weft yarns (Todd 1902, 47) ................................202 Ill. 106 Weaving patterns and warp sequence (Todd 1902) ...................................................................................................203 Ill. 107 Diagrammatic modelling process applied for digitally woven structures...............................................................204 Ill. 108 Left: Plain weaving pattern, Module A-over 1: right: Module B-under 1 ..............................................................205 Ill. 109 Left: Plain weave modular distribution pattern, right: gradual offset pattern for definition of cell height ......206 Ill. 110 Left: 3D model of a plain weave structure with local gradient, right: gradient map ............................................207 Ill. 111 Left: module distribution in a twill weave, right: grid distortion with a gradual decrease in x and y-values....209 Ill. 112 Twill weave pattern applied to deformed cellular matrix with gradual deformation of initial grid structure ..210 Ill. 113 Differentiation of thread radii depending on line lengths.........................................................................................211 Ill. 114 Left: Zcorp print of test geometry, right: composition of multi-layered composite............................................212 Ill. 115 Material deterioration of a composite polymer structure..........................................................................................212 Ill. 116 Parametric definition of plain knit ................................................................................................................................217 Ill. 117 Geometric definition of a simple knit in Excel...........................................................................................................218 Ill. 118 Digital model of plain knitted cells ...............................................................................................................................219 Ill. 119 Tubular intersection with a radius of 0.035 in a given cellular dimension of 1x1x1 ............................................219 Ill. 120 Left: initial graphic map, middle: height-field from bitmap, right: retrieval of z-coordinate information .......220 Ill. 121 Relationship between cellular height and movement of the knit ............................................................................221 Ill. 122 Gradual cellular offset based on scaled z-coordinate values ....................................................................................222 270

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Ill. 123 Deformed surface with cellular distribution of plain stitch ......................................................................................223 Ill. 124 Knitting path at three sample locations........................................................................................................................224 Ill. 125 Rule 90 cell conditions 1-8 (Wolfram 2002, 25) .........................................................................................................225 Ill. 126 CA pattern based on rule 90...........................................................................................................................................226 Ill. 127 Local cellular deformation based on CA pattern sequencing...................................................................................227 Ill. 128 Top view and perspective of distorted and undistorted geometry ..........................................................................228 Ill. 129 Final knitted sample with CA pattern applied.............................................................................................................229 Ill. 130 Homeomorphic transformations of cellular components under geometrical and cellular alterations..............230 Ill. 131 Scaling of binary matrix values for cellular motion control ......................................................................................232 Ill. 132 Root surface from point cloud ......................................................................................................................................232 Ill. 133 Digital model of plain knit with cellular deformation ...............................................................................................233 Ill. 134 Top right: AF of knitted geometry, top left: support structure, bottom: cellular variation ................................234 Ill. 135 Selection of encoded knitting components and numerical patterning ...................................................................236 Ill. 136 Graphical encoding of knit cells with descriptive nomenclature of thread structure ..........................................237 Ill. 137 Cellular clusters or interdependent knit configurations ............................................................................................238 Ill. 138 Left: overlay of image source and knit pattern, right: demonstrator patch ...........................................................239 Ill. 139 Data-scaling on three hierarchically interconnected levels .......................................................................................240 Ill. 140 Created knitted structure with CA-based information. Red areas show pattern change.....................................241 Ill. 141 Re-application of the patterning, cellular height and local deformation on an alternative cellular matrix.......242 Ill. 142: Right: piped segment, left: digital model of the extracted area from the final model .........................................243 Ill. 143 Left: knitted wall segment, right: detail with cavity ....................................................................................................244 Ill. 144 Cavities for tensile rods in printed column component (design by James Gardiner/Faan Studio) ..................245 Ill. 145 McKibben muscles (Verrelst et al. 2000) .....................................................................................................................273 Ill. 146 Systematic drawing of constricted pneumatic structures (Otto 1995) ....................................................................274 Ill. 147 Left: RP test with varying skin thickness, right: sample with structural limiters of varying dimensions.........276 Ill. 148 Design of multi-material structural limiters .................................................................................................................277 Ill. 149-3D Connex print of knot................................................................................................................................................277

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Appendix

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Excursus: Additive fabrication of pneumatic structures Deployables with a graded performative morphology have contributed to the scope of the architectural toolset in the past. The interplay between elastic skins and structural limiters sees contemporary application on many scales.

Smaller performative pneumatic structures have gained attention in the past for their ability to mimic the action of human muscles and for their fluid performance of controlled locomotion. These pneumatic muscles have been developed by Festo (Teschler 2006), among others, and extend the efficiency of historical air-driven mechanical entities like the McKibben Muscle (Verrelst et al. 2000), which was developed for prosthetic devices in the 1950s (Ill. 145). Such “air muscles” have performance characteristics similar to the human muscle, since the force exerted decreases as the muscle contracts. This is due to the change in the interweave angle of the braided mesh as the muscle contracts—as the mesh expands radially in a scissors-like motion it exerts less force due to the weave angle becoming increasingly shallow as the muscle contracts.

Ill. 145 McKibben muscles (Verrelst et al. 2000)

Frei Otto’s Institut für leichte Flächentragwerke delivered a broad range of experimental studies and mock-ups of convertible “pneu” structures in different scales (Institut für leichte Flächentragwerke 1976). Its research intensively investigated an implementation of pneumatic constriction methods (Ill. 146) achieved by a combination of elastic inflatable materials with additional materials in the shapes of nets, pressure rings, inner bracings or inner strutting.

These composite pneus are assembled according to a distinct technological sequence and within a range of readily available mostly standardised materials. Since inflatables rely on membranes that are constructed from planar material, the required fitting seams and unrolling patterns become a structural issue and frame the scope of possible

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geometric solutions.97 Large-scale pneumatic structures thus consist of an assembly of unrolled surface patterns and must be designed under this constraint.

Ill. 146 Systematic drawing of constricted pneumatic structures (Otto 1995)

Additive fabrication processes now allow the geometric definition of highly irregular inflatable skins with varying, performance-based expansion properties that cannot be manufactured with classical production methods. The option to differentiate the material composition of the expansive material allows finer tuning of the performative criteria, since the elasticity of the material under tension can be driven parametrically. The material thickness and its structural composition can be tuned to allow a locally adjustable pneumatic performance. This new manufacturing option merges different manufacturing streams into a single fabrication moment, allowing the implementation of highly complex geometric entities of varying elasticity in a subcutaneous position. The morphology of such a skin that encodes a specific dynamic performance is based solely on -

the geometric constraints imposed by the modelling software,

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fabrication effects on the materials internal composition and

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constraints imposed on the individual manufacturing technology.

The latter two address the potential anisotropic material properties that are derived from the vertically layered material disposition process and the strategies required for support-structure removal. As stated, the multiple manufacturing processes that are usually needed for the fabrication of inflatable composites are merged through additive fabrication into a single process that allows the realisation of different, characteristic geometric solutions.

The fabrication of multiple material properties with highly complex three-dimensional geometries can now be

97 Contemporary sailing technology actively integrates reinforced stitching styles that correspond with the expanded structural performance. Further information be found in McQuaid (2005) 274

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achieved without the usual sequential lamination process. These manufacturing possibilities expand the scope of performance of inflatable skins, since the geometric constraints are significantly smaller and allow the gradual distribution of materials that can lead to local functional performance.

Several advantages render a future application of additive fabrication in the field of pneumatic dynamical structures interesting and will be discussed comprehensively here: -The dead load of the material that is employed for the construction of pneumatic structures is negligible compared to conventional structural solutions. This factor enables the printed model to be analysed under rather realistic conditions affecting their structural and geometric performance. The combination of additive with inflatable technologies facilitates the realisation of potential large-scale objects. By fabricating folded skins, the scale of the printed object can be increased significantly through inflation. Additionally, the effects of all kinds of creased geometries can be studied, depending on the character of the folds. As elasticity becomes a digitally controllable parameter, the complex interaction of truly dynamic elements can be realised.

-The model relies not on a hierarchical structural system composed of differently articulate load-bearing systems, but on a dynamic interaction of self-stiffening members. The spatial arrangement defines the performance domain of the overall structure, which is further articulated by the discrete configuration of the local expansion behaviour of the skin.

-Elastic inflatable structures have rarely been applied in building construction. The reason may be found in the change in stiffness that occurs with varying loads, entailing a lack of reliability. The most widespread industrial structural application for elastic pneumatic elements can be found in car tyres. The success of the system can be found, above all, in two qualities: the more rigid tyre limits the soft inflatable tube. The whole system is redundant. The technology of printing different materials allows for a more sophisticated distribution of limiters. Redundancy will be given by the overall design of the investigated structures.

-Since additive fabrication technologies have greater freedom in the design of skins, their independence from the usual fabrication constraints of air tight membranes means that a broader bandwidth of possible skin designs can be fabricated. Here again, the topic of support-structure removal has to be taken into account.

The first study created a skin with varying thicknesses as based on a 2D numerical matrix. This test is easy to control using contemporary CAD tools, but more complex to fabricate with conventional manufacturing processes since it requires the fabrication of casting moulds. In the study a rectangular base surface was sub-divided into an evenly spaced grid of the U and V distributions of the surface. The numerical matrix was then applied to the sub-division grid and delivered a matrix-dependent offset of the surface-normal within a predefined numeric range. The surface could be easily closed on the remaining edges and then printed with an elastic material. For this study the elastic TangoBlack material from Objet was used (Ill. 147). The complexity of these skins can be further increased to demonstrate the advantageous properties that can emerge with additive fabrication technologies. The field of continuous complex surfaces without intersections can provide an interesting field for future research activities on the fabrication of such pneumatic structures under the existing manufacturing and material constraints.

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Ill. 147 Left: RP test with varying skin thickness, right: sample with structural limiters of varying dimensions

A further definition of such membranes can be achieved by coupling stiffer limiter geometries (Ill. 147). These can be defined in such manner that they act upon the surface to affect inflation behaviour or dynamic form-changing potential. Such processes can be realised using two simultaneously printed polymers of different hardness. In a physical test graded distribution of circular limiters with changing diameters was printed. Three points on the surface were identified as areas of maximum flexibility, with a gradual change towards stiffer zones within the composite, expressed by an increase in the radii of the stiffer plates. These relational definitions are easy to set and model, yet the print quality still remains an obstacle for functional applications. The emerging problems with the print technology will be further highlighted in the description of the next test.

A subsequent test looked into controlling such a membrane by applying irregular structural limiters composed of a different—usually harder—print material. For the test a knot structure was modelled with air intake nozzles to drive the internal pressure level.

The parts of the membrane surface to expand first were endowed with physical properties correlated with the stress distribution derived from the initial curvature. The membrane tensions of an air-supported dome structure under the surface loading of internal pressure can be indicated by the expression (Dent 1971, 51) T = ( Pi * R ) / 2 with T=Surface curvature; R=Radius; Pi=Inner membrane tension Accordingly, the centre parts of the expansion surface were equipped with an elastic material encircled by two surfaces of varying flexibility (Ill. 148). The first version of the knot contained individual air intake nozzles and two types of joint systems for attachment of the neighbouring knots. The individual pressure levels of each node would drive adjustable areas of surface expansion that would be correlated with the performative quality of the overall structure.

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Ill. 148 Design of multi-material structural limiters

The condition for a successful structural application thus is fulfilled by the reinforcing parts or limiters, which are built up by less elastic material. These parts also act as a tensile net, a common system in building construction to reinforce inflatable structures and to manipulate their form (Herzog 1976)

Ill. 149-3D Connex print of knot The first test print (Ill. 149) delivered a series of important insights on the geometric and material constraints that impact future designs of such structures.

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-

The geometric accuracy of the printed geometries is important to prevent minimal capillary gaps.98 The occurrence of this problem can be prevented in two ways, either through a mathematical description of the surface,99 or through a change in the knot’s morphology. The material thickness of the layered surfaces has to be rather sturdy to prevent cracks, and opposes a facile inflation process by requiring a high level of air pressure.

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Material tear resistance is highly dependent on the build direction. The evolving material shows anisotropic behaviour. An analysis of the printed-out model clearly exposed the different material properties, which range from stiff to different degrees of elasticity.

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The first test created material differentiation through clearly separated areas of different elastic properties on the skin’s surface. The limiters were placed inside the membrane with the same thickness. During the printing process it became visible that the border between different material areas was vulnerable to tearing and could potentially affect the airtight properties of the material.

Although technically correct, the printed samples deliver very poor performance and show high brittleness that precludes their use as a fully functional component. Material deterioration can be witnessed over time that affects form stability, evinced by the emergence of smaller and larger cracks that lead to the object’s deterioration under mechanical stretching and bending. Research into these interesting composites is nevertheless valuable since it makes the existing material deficits more prominently known so that they can be improved and potentially fixed over time.

Conceptualisation and early testing of these materials can then be employed for later, more functional implementation into components with graded performance of some kind.

98 The initial saddle was modeled as a patch surface defined by six edge lines. The software delivered a very good approximation of the edge conditions, but not a geometrically precise result. Due to these inaccuracies, which were further amplified through the surface offsets, capillary gaps were created that materialised as cuts in the printing process. These cuts conflict with the idea of a pneumatic component, for obvious reasons.

99 This surface generation process is not defined by formgiving rail lines, which are used to configure a dependent surface configuration, but relies instead on a mathematical description of the surface itself. The surface therefore does not contain any of the edge lines that are usually sensitive in the surface offset process.

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