Biomimetics sally, cesar, yorgos, katya

Emergent Technologies & Design Biomimetics Documentation Lobster Shell | 2016 Sally Al-Badry, Yorgos Berdos, Katya Bryskina, Cesar Cheng

CONTENTS 0. ABSTRACT 0. INTRODUCTION 0. AIMS AND METHODS

P.04 P.05 P.06

1.0 BIOLOGICAL MODEL _1.1 LOBSTER EXOSKELETON _1.2 HIERACHICAL ORGANIZATION _1.3 ORGANIZATION PRINCIPLES _1.4 FIBER ARRANGEMENT _1.5 2D PATTERNS

P.08 P.08 P.09 P.11 P.12 P.13

2.0 MATERIAL EXPLORATION _2.1 INITIAL MATERIAL EXPLORATION _2.2 MATERIAL ORGANIZATION

P.14 P.17

3.0 MATERIAL EXPERIMENTS _3.1 EXPERIMENT 1 _3.2 EXPERIMENT 2 _3.3 EXPERIMENT 3 _3.4 EXPERIMENT 4 _3.5 EXPERIMENT 5

P.18 P.20 P.22 P.24 P.26

4.0 MATERIAL SYSTEM _4.1 LOCAL PARAMETERS _4.2 REGIONAL PARAMETERS _4.3 GLOBAL PARAMETERS

P.28 P.30 P.32

5.0 CONCLUSION _5.1 CONCLUSION

P.36

ABSTRACT

The exoskeleton of crustaceans and other arthropods provide structural and mechanical support to these animals and enable their movement through the formation of joints as well as attachments for specialized parts of the animal which serve diverse functions. In natural systems, performance variation and multi-functionality are achieved with, often times, one single material1. It is important to note that the success of these materials is not due to its composition per se but due to the way the material is organized across multiple scales2. In this work, the shell of the American Lobster ( Homarus americanus) from the family of crustaceans was selected as the object of study. The entire lobster shell is made from a single composite material called chitin in the form of polymer fibers.

The goal of the project was to gain an understanding of the fiber organization in the lobster shell and abstract general organization principles that were later translated into a design strategy to develop a material system for architectural applications.

In the process of developing the system, both analogue techniques of form-finding and digital tools for analysis were utilized to establish a design strategy that creates performance differentiation

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through local variations in material organization. Parallel to this investigations, several experiments on material behavior were conducted, specifically looking at the elastic properties of rubberlatex working in combination with 2D fiber patterns that were designed to react to the pre-stretched active forces of latex and induce 3D form upon release. Finally, a material system of variablestiffness which acts in a similar way to the natural systems found in nature is proposed and a strategy to produce variable states of stiffness is outlined.

Keywords: Lobster Shell; Variable-Stiffness System; Material

NOTES. 1. P. 883 D. Raabe a et al. Preferred crystallographic texture of a-chitin as a microscopic and macroscopic design principle of the exoskeleton of the lobster. Acta Biomaterialia 3 (2007) 882–895.

2. P. 92-95 Jeronimidis, George. Emergence: Morphogenetic Design Strategies. Chichester: Wiley-Academy, 2004. Print.

INTRODUCTION Artist, Paul Veroude, VS2

0.1 BACKGROUND: The way materials are used in nature for the construction of biological systems is fundamentally different from most man-made material systems which often times dismiss the active properties inherent in the material when arranged in particular geometric configurations. Man-made designed objects generally involved hundreds of distinct parts and multiple materials, each of which have their own construction logic and often times serve a single function. A typical automobile has about 30,000 parts and “[uses] different raw materials and different manufacturing processes”1.

In contrast, natural systems use very few materials and their parts and manufacturing process has been optimized to serve multiple functions. Nature’s design intelligence lies not so much in what the material is, but rather in how the material is used. In nature, the deliberate disposition of material in certain types of arrangements enables the material capacities to act structurally and respond to external forces. When studying biological systems, “[it] makes little sense to distinguish between material and structure” 2. The integration of material, form and performance is evident in many biological systems such as bones in vertebrates, wood branches in trees or arthropod exoskeletons.

This work focuses on the study of the exoskeleton of the American Lobster (Homarus americanus) which is a continuous yet differentiated surface that serves multiple functions. In the lobster exoskeleton different regions of the shell have different degrees of stiffness responding to specific mechanical and functional requirements, for instance, the crusher-claw (used to crush the shell of its prey) is stiff and strong while segments of the tail are soft and flexible to allow for motion. The most striking observation and the basis of our present study is the fact that all the parts of the shell despite their difference in function are all made from the same material; a fiber polymer called chitin which is organized across multiple scales to produce variation in form and differentiation in performance.

NOTES. 1. TOYOTA CO JP, FAQ WEBShttp://www.toyota.co.jp/en/kids/faq/d/01/04/E. Online.

2. P. 92-95 Jeronimidis, George. Emergence: Morphogenetic Design Strategies. Chichester: Wiley-Academy, 2004. Print.

3. P. 391–400. Helge-Otto Fabritius et al. Adv. Mater. 2009, 21 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim,

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0.0 AIMS & METHODS

0.2 AIMS AND OBJECTIVES Inspired by nature’s efficient use of material in the process of form generation [1] this project aims at understanding and translating design principles from the biological model of the lobster shell into a design approach that supports the integration of material, form and performace. [2] This project also seeks to use this approach to produce a variable-stiffness system with the possibility of architectural applications.

0.3 METHODOLOGY The deisgn and development of the project involved a combination of digital tests and physical experiments. Digital tools were used both for production and analysis. The design and analysis of the 2D patterns was carried out with the aid of generative algorithm design tools in the Rhino/Grasshopper platform. The challange of translating 2D digital design to 3D form in the computational environment required us to also rely on numerous physical experiments to understand material behaviour and prove the feasability of construction logics developed digitally. Even though the entirety of the project was not fully computed from 2D to 3D form, the development of the project would not have been possible with the use of analogue techniques only. Computation and algorithmic design were essential for fabrication processes and design development. Neither, we believe the entirety of the project would have been possible with out the use of analogue techniques of form-finding and physical material testing.

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As part of the material research exploration, we selected rubberlatex for its elastic properties and its capacity to store force when streched. The idea was to use latex as a base membrane onto which 2D patterns would be applied in order to produce deformation due to pattern deisgn and material orientation. Latex sheets were tested as a ready-made product sold in conventional stores and available in various thichnesses (.38mm, .50mm, 1mm). Liquid latex was also used to fabricate custom latex sheets inside which other materials were embedded, the production of these custom sheets was carried out as in-house production experiment with a custom made plastic frame pool and other basic production instruments such as brushes and rollers. For the design of 2D patterns we employed various types of materials with a wide range of structural and elastic properties to work in combination with latex. For these experiments we employed polypropelene sheets in various thicknesses ( 1mm, 1.8mm, 3mm) and Metal piano wire in (.38 mm).

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1.0 BIOLOGICAL MODEL

times mineralized with calcium carbonate to increase its rigidity and structural capacities1.

The cuticle makes up the major part of the integument (skin) of arthropoda. Overall the cuticle is rigid and inhibits the animal from growing, for this reason arthropods replace it periodically by molting. The cuticle is secreted from a basement membrane [Fig2] which starts as a flexible layer of chitin. This thin flexible cuticle forms the main structure in parts of the shell where flexibility is 1 required such as joints between rigid parts of the skeleton. Other parts of the shell demand the cuticle to be more rigid such as armored regions for protection or instrumental parts such as the claws, these harder areas are mineralized with calcium carbonate2.

FIG. 1. Schematic drawing of the morphology of Homarus americanus according to Carpenter.6

1.1 LOBSTER EXOSKELETON (CUTICLE) Arthropods are a group of invertebrate organisms characterized by having a segmented body, an exoskeleton and joined appendage.

These group of animals includes: insects, arachnids, myriapods and crustaceans. Arthropods are the most diverse and species-rich group of animals on earth whose body has been adapted to operate in wide range of environments. A key design feature in these animals is the exoskeleton also known as the cuticle. In the lobster as in other arthropda, the cuticle provides protection and structural support to the animal. The material composition of the cuticle is chitin, often

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The cuticle is primarily divided into three main sections, the epicuticle, exocuticle and endocuticle [figure 2]. Acting as a barrier the epicuticle is a thin waxy layer that isolates and protects the animal from the exterior environment. The next two layers, the exo and endocuticle, are responsible for providing support and carrying mechanical loads3. At a micro-level, the cuticle of crustaceans is organized in a complex hierarchical structure that can be observed under the microscope. This structural hierarchy allows the material composite to provide a wide range of functions and differentiate across regions of the shell.

1. Artropods. Encyclopedia Britannica http://www.britannica.com/animal/arthropod. Online.

2. P. 302. D. Raabe a et al. The exoskeleton of the lobster homarus americanus as an example of smart anisotropic biological material. Max Planck institute for iron research. Acta Biomaterialia 3 (2007) 301–309.

3. P. 303. D. Raabe a et al. The exoskeleton of the lobster homarus americanus as an example of smart anisotropic biological material. Max Planck institute for iron research. Acta Biomaterialia 3 (2007) 301–309.

Epicuticle Exocuticle Endocuticle Epidermis Basement Layer

FIG. 2. Redrawn from: Arthropod Exoskeleton: Cuticle and Joints https://www.cals. ncsu.edu/course/zo150/mozley/fall/exoskelet.jpg

FIG. 3. Schematic presentation of the hierarchical microstructure of the cuticle of the lobster H. americanus. From D. Raabe et al. Acta Biomaterialia 3 (2007) 882-896.

1.2 HIERARCHICAL ORGANIZATION An important feature in the design of the exoskeleton of the lobster is the hierarchical structure that occurs at multiple length scales.

Natural systems such as the lobster shell are able to produce material assemblies that vary in shape, size and spatial distribution1.

This capacity for variation leads to the possibility of establishing parametric relations between the constituent parts and the whole. Changes in the arrangement of material at one level have a direct impact on the order of the entire system. The principle of hierarchical organization and the possibility of having parametric relations between elements in a given system underlined our future explorations in the development of our project.

Within the lobster cuticle, six main different structural levels can be observed. The first level of order, at the molecular scale, begins with long chains of chitin molecules. In the second structural level these chains of chitin are wrapped in proteins and arranged in the form of Nano fibrils of 2-5nm and 300 nm length. In the third level these Nano fibrils cluster to form long chitin-protein fibers of 50 -300nm diameter. In the fourth level of hierarchical order these chitin fibers area arranged in a planar honeycomb array. In the fifth level, planes fibers are stacked on top of each other and rotate forming a structural arrangement usually referred to as twisted plywood or Bouligand pattern. In the sixth level, a complex structure is created by the gradual rotation of this planes forming the larger sections previously described as the endocuticle and exocuticle2. Some of these organization principles were studied and abstracted to inform the design strategy for the development of our material system.

1. P. 391–400. Helge-Otto Fabritius et al. Adv. Mater. 2009, 21 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2. P. 303. D. Raabe a et al. The exoskeleton of the lobster homarus americanus as an example of smart anisotropic biological material. Max Planck institute for iron research. Acta Biomaterialia 3 (2007) 301–309.

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PRINCIPLES FROM BIOLOGICAL MODEL LOBSTER SHELL | FIBER PLANES

1.0 BIOLOGICAL MODEL 1

2

UNI-DIRECTIONAL

FORCE DIRECTION

10

CURVATURE BENDING

ROTATION MULTIDIRECTIONAL

ISOTROPY DISTRIBUTED LOADS

3

DENSITY

STRENGHT

1.3 DESIGN PRINCIPLES Through local material differentiation the shell of the lobster is adapted to suit specific functional requirements.

As discussed earlier (p.8-9), the way in which material is organized leads to variation within the material system which in turn can be used to respond to specific mechanical and functional demands. The diagram on the left (p.10) represents three main design principles that were abstracted from the biological model and used as a point of departure for the development of a new material system. In the lobster shell, variation in the position and orientation of the fibers responds to particular requirements.

(1) Areas of the shell that respond to a specific load path are arranged in unidirectional layer configuration producing an anisotropic fiber arrangement in order to transfer loads more efficiently [FIG1].

In contrast, (2) areas that require an even distribution of loads in multiple directions

show an isotropic fiber configuration in which layers of fibers are stacked and rotated in a helicoidal arrangement[FIG 2]. Furthermore, (3) variation in density and concentration of material can lead to increase in strength and used to restrict movement [F.IG3] These were the three core priciples used in future experiments to guide the design of patterns in the development of the project.

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1.0 BIOLOGICAL MODEL

1.4 FIBER ARRAGEMENT EXPLORATION Geometric explorations began as a twodimensional design exercise. Informed by the organization principles abstracted from the lobster shell, this exercise aimed at creating fiber configurations and establishing parametric relations that produce difference and variation in material arrangement. In the computational environment “fibers” were represented and constructed as spline-curves. Using computational tools, an algorithm was developed to control various parameters of the curveelements. Parametric relations were set in accordance to the organization principles in the hierarchical structure of the lobster shell. The primary design parameter used in the pattern generation were: density (number of curves), intervals, frequency, orientation (curve direction) and gradual transitions.

These two-dimensional patterns were designed to react to a prestretched base membrane and generate three-dimensional forms as a result of the pattern.

FIBER ARRANGEMENT ORIENTATION AND DENSITY

1

1

HORIZONTAL UNI-DIRECTION

2 2 DIRECTIONAL AND GRADUAL DENSITY

3 3 GRADUAL DENSITY

4 4

PORE CANALS DIFFERENTIATION

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INTERTWINED MULTI-DIRECTION

ORTHOGONAL GRID

1.5 TWO DIMENSIONAL PATTERNS

5

6

7

8

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Figure 1, the diagram explores a design configuration that starts horizontally oriented (uni-directional), which then gradually transitions to zone of crossed angled members and finally terminates as an equally spaced orthogonal grid.

Figure 2, the diagram shows a diamond grid configuration with increased density in two directions. The central zone of the pattern from top-to-bottom is compressed while at the same time the pattern gradually increases in density from left to right.

Figure 3, the diagram shows a fiber configuration in which the diamond pattern increases in density along one axis only.

Figure 4, the diagram is built upon the idea of thickening the fibers in a stretched honeycomb configuration and gradually subtracting material from the center to the ends.

Figures 5-9, These set of diagrams show possible variations of fiber configuration consisting of curves that change direction locally from straight elements into a periodic curve.

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LIQUID LATEX + PIANO WIRE

2.0 MATERIAL EXPERIMENTATION

LIQUID LATEX + PLASTIC MESH 1. LIQUID LATEX + PLASTIC MESH

2.1 INITIAL MATERIAL EXPLORATION Several material experiments were conducted with the purpose of understanding the relationship between material behaviour and geometry. As a base membrane rubber-latex was selected for its capacity to store elastic energy when streched. This base membrane would be pre-streched or post-streched to induce deformation according to the design of the patterns.

For the physical fabrication of the patterns several materials were explored to evaluate the posibilities offered by their properties. The materials used for this experiment were: metal piano wires, plastic polyproperlene sheets and plastic mesh. Latex was used both in liquid and solid form which allowed us to test the possibility of embedding the fibers into the latex or applyng them to the latex as a secondary layer.

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LATEX LIQUID SHEET LATEX + PIANO + PIANO WIRES WIRE 2. LIQUID LATEX + PIANO WIRES

LATEX LIQU SH

SH LATEX SHEET + PIANO WIRES C MESH LATEX SHEET + PIANO WIRES 3. LATEX SHEET+ PIANO WIRES

LATEX SHEET + POLYPROPYLENE LATEX SHEET + POLYPROPYLENE 4. LATEX SHEET+ POLYPROPYLENE

1. In the first experiment, liquid latex and a plastic mesh membrane were employed to create a sheet of material with the mesh fibers embedded in the latex. By shifting the individual fibers into an undulating pattern arrangement the result we achieve is a reinforced latex membrane which reacts to tensile forces when post-streched creating 3D peaks and valleys across the surface of the material.

2. The next experiment was carried out using liquid latex and piano wires. A weaved pattern in which the space between the piano wires increases across the material is layed out. The combination between these two materials produces a reinforced sheet of latex that performs differently according to the changing spacing between the wires , however, it does not maintain its deformed shape without the use of anchor points at its boundary edges.

3. For this experiment a sheet of latex was pre-streched in two directions and a piano wire weaved pattern was applied onto it. When the bidirectional stress is released the sample deforms and finds its final form. The final global geometry results in a doubly curved surface in a defined stable state.

4. For these experiments a pre-stretched latex sheets in combination with a lasercut polyproperlene 2D pattern were used. After the pattern is applied, the composite sheet deforms and holds its final form in a stable state. Thickness of material as well as geometrical configuration play a crucial role in the form-defining process. In the case of polyproperlene, a sheet material that is available in various thicknesses and can be cut to custom dimensions, the parameters that guide form definition can be better controlled.

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FIG. 1. process of liquid latex being poured onto metal pattern with changing density.

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2.2. MATERIAL ORGANIZATION PRINCIPLES “Everything which happens and everything which appears is correlated with orders of differences: differences of level, temperature, pressure, tension, potential, difference of intensity” 1.

(Deleuze) Material organization and differentiating behaviour in various scales are crucial factors that need to be understood and re-determined in order to challenge the way that architectural form has traditionally been concieved, produced and reproduced. In this particular exploration , the selected materials and their individual properties are not considered as design constraints but as additional design parameters that could express effectively complex relations between structure, geometry and fabrication.

With the proposed form-finding system, that will be further explained in the current work, we aspire to acquire control over the way that 2D patterns can be translated into 3D formations, harnessing FIG. 3. Resulting geometry from 2D metal pattern applied onto pre-streched latex sheet.

the tension provided by prestreched membranes.

Although we overall control of the translation of 2D patterning into 3D forms at a local level, we could assert that the global formation still follows a self-organizational logic. In the context of biological systems, self-organization could be defined as “a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower-level components of the system. Moreover, the rules specifying interactions among the system’s components are executed using only local information, without reference to the global pattern.” 2 In our particular case, the global system is sensitive and nonlinearly responsive to the initial pattern at a local level as well as to the connections between each element on regional level and to the global aggregation of the structure.

1.P. 222. G. Deleuze, Difference and Repetition, Bloomsbury Academic; 2nd Revised edition edition (2014) 2. P. 8. S. Camazine et al, Self-Organization in Biological Systems, Princeton University Press (2001)

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3.1 EXPERIMENT 1 1

2

3

EVENLY DISTRIBUTED ONE DIRECTION

STRECHING 1 DIRECTION

STRECHING

1 1 Parameters

Frame size: 190*120mm Latex sheet: 250*160mm Stretching: 40mm

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Results: double curvature Arc height: 50mm

2 Parameters

Frame size: 190*120mm Latex sheet: 250*160mm Stretching: 30mm Results: double curvature Arc height: 38mm

3 Parameters

Frame size: 190*120mm Latex sheet: 250*160mm Stretching: 20mm Results: double curvature Arc height: 30mm

3.1 PHYSICAL EXPERIMENTS - 1 As the project investigates the way in which the tension caused by pre-streching an elastic membrane can deform a twodimensional pattern resulting a doubly curved surface, important decisions were made regarding the material selection.

Five main sets of experiments were conducted, each aiming to investigate episodes of varying complexity produced by the same apparatus. The materials selected for those experiments were elastic membranes-sheets made of rubber latex , polypropylene-sheets and strong, fast-acting adhesives (“superglue� based on cyanoacrylates). The latex sheets were 0.38mm thick while the polypropylene sheets were 1mm thick. Different patterns were designed and laser cutted on the polypropylene sheets while the latex sheets were carefully streched on various lengths. The two materials were bonded with superglue applied on the total surface of polypropylene pattern and then released

1- Different Stretching amount: The initial experiment demonstrates the latex membrane when it is (pre)streched in one direction, with varying prestreching factors. The pattern on the polypropylene consisted of evenly distributed vertical elements-fibers, perpendicular to the direction of the streching. All these three experiments resulted in a doubly curved surface, as shown on the opposite page. Increasing the prestreching of the latex sheet, progressively increased the resulting three dimensional deformation.

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3.2 EXPERIMENT 2 1

2

3

EVEN

CENTER

SIDE

STRECHING 1 DIRECTION

1 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm

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Results: single curvature Arc height: 25mm

2

Parameters Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm Results: single curvature Arc height: 65mm

3 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm Results: single curvature - Displacement Arc height: 70mm

3.2 PHYSICAL EXPERIMENTS - 2 2- Different Fiber Arrangement: In this experiment the latex membrane was streched in one direction - in similar way that it was streched for experiments-1. The pattern on the polypropylene is now consisted of linear elements which intersect perpendicular to each other and to the outer frame. The density of the pattern in each one of the three tests shown on the opposite page is different. On the first case the fibers are evenly distributed both vertically and horizontally, on the second the pattern gets more dense towards the centre of the panel and on the last case more fibers are gathered on the upper left side of the panel. Although the latex membrane is equally streched in those 3 cases,

the three dimensional form that appeared after we released the membranes was significantly different for each polypropylene pattern. The panel with the evenly distributed fibers was slightly deformed. The 3D results were slightly different between the second and third panel. All the three produced surfaces were mainly single curved (minor double curvature was achieved only in some areas of the latex membrane, between the polypropylene fibers).

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3.3 EXPERIMENT 3 1

2

3

EVEN

CENTER

SIDE

STRECHING 2 DIRECTION

1 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 100mm (equally stretched)

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Results: double curvature Arc height: 60mm

2 Parameters

Frame size: 190*120mm Latex sheet: 250*160mm Stretching: 100mm (equally stretched) Results: double curvature Arc height: 60mm

3 Parameters

Frame size: 190*120mm Latex sheet: 250*160mm Stretching: 100mm (equally stretched) Results: double curvature Arc height: 90mm

3.3 PHYSICAL EXPERIMENTS - 3 3- Different Fiber Arrangement: In this experiment, the latex membrane is homogeneously (in both directions) and equally stretched in all the three cases.

The three patterns used are identical with those used for experiments-2.

The resulted surfaces from this set of experiments were much more deformed in comparison to the surfaces produced by the respective panels from experiments-2. Global double curvature was achieved in all the cases. The first two panels were similarly deformed. The third one, apart from the global double curvature, showed profound regional double curvature, where the orthogonal pattern was sparser.

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3.4 EXPERIMENT 4 1

2

3

TRIANGLE ONE DIRECTION

CIRCLE ONE DIRECTION

CIRCLE TWO DIRECTIONS

STRECHING 2 DIRECTION

1 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm

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Results: double curvature - controlled deformation

2 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm Results: double curvature - peaks and valleys in both directions

3 Parameters

Frame size: 190*120mm Latex sheet: 250* 160mm Stretching: 40mm Results: single curvature - controlled deformation in one direction.

3.4 PHYSICAL EXPERIMENTS - 4 4- Different Frame conditions: The next series of experiments demonstrate the relationship between three different patterns applied to the pre-stretched membrane and the resulting curvature produced upon release. The panel used at the first experiment consists of a triangular frame and the pattern with one directional fibers running from one side of the panel towards the opposite vertex. The result achieved, as shown on the opposite page, was a doubly curved surface, with the curvature being more evident on the axis perpendicular to the fibers’ direction.

The second panel had a circular frame that contained one directional curved fibers (hyperbolic transition pattern).

After this panel was released, a doubly curved surface with peaks and valleys in both sides and directions was generated.

The third experiment was based on the second one with the addition of intersecting fibers on the vertical direction. The resulted surface was single curved, along the axes (horizontal) that contained more fibers than the other.

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3.5 EXPERIMENT 5

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3.5 PHYSICAL EXPERIMENTS - 5 5-Principal stress lines The methodology used for this experiment deviated from the analytic proccess that the rest of the experiments were based on. In this particular case, a three dimensional surface was created was designed using Rhinoceros. This surface was touching the ground at four points, which coincide with the edges of the square shown. Then using the Karamba plug-in for Grasshopper and setting the four above mentioned edges as anchor points of the structure, the principal stress lines of the surface were extracted.

These lines, after being rationalized and simplified, were used as guidelines for the pattern that polypropylene panel contained.

Then the panel was glued on an homogeneously streched latex membrane. When the panel was released a doubly curved surface arised.

This surface was almost identical with the initial one created in the virtual space of Rhinoceros.

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4.0 MATERIAL SYSTEM 4.1 Local Parameters The results attained in previous experiments on material testing provided us with a basic understanding on the interplay between material behavior and geometry. Material properties such as thickness (crosssectional area) and elasticity (amount of stretching) were evaluated against geometric operations in the design of patterns. Based on these results we began to establish relations between material thickness and pattern orientation which allowed us to develop a strategy to control the design parameters in a more intentional way.

LOCAL PARAMETERS diagram [Fig 1] the two sets are represented with letters set [A,B,C,...] and [0,1,2,3,...]. The horizontal set of fibers locally change direction and are arranged in the form of a periodic curve with parametric control over curve frequency and amplitude. The vertical set of fibers are kept parallel to each other andLOCAL uni-directional PARAMETERS while changing in density and interval distribution. This fiber arrangement 1 2 3 4 provides the opportunity to establish an additive system that can grow in two directions and Acreate gradual B transitions from single directional C to multidirectional material D configurations.

Based on the organization principles abstracted from the LOCAL lobster PARAMETERS exoskeleton, the design is organized in a hierarchical order starting from 1 2 3 4 setting local relations between the smallest sub-units in the system.

A B local scale, the smallest subC in the system consist of D two sets

At a units of fibers (curves) initially oriented perpendicular to each other. In the

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5

1

A B C D

2

3

4

1

2

3

4

5

1

2

3

A B C D

A B C D

5

1

2

3

4

5

A B C D

A B C D

5

1

A B C D

1

2 3 4

5

6

7

8 9 10 11

2 3 4

5

6

7

A B C D

A B C D

A B C D

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DEFORMATIONS 4.2REGIONAL REGIONAL MODEL

Element 1: Strength, Frame, Connector

Element 2: Stiffening, Surface articulation

Element 3: Flexibility, Folding

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REGIONAL PARAMETERS Graphical representation of the different fibres arragment inside each structural component - cell. The local changes of the fibres arrangement are driving the differentiating global behavior.

Intersecting fibres, changing density.

This formation generates stiff areas with small degree of curvature. The degree of curvature is proportional to the density of the grid produced by the intersecting fibres

Longitudal fibres, straight, one-directional, gradual density The density of the of the longitudal fibres is controlling the section of the global geometry, the arrangement of the flexible and stiffer areas.

Where the longitudal fibres are not intersected, local deformation is being produced. The degree of curvature in the deformed area is proportional to the density of the vertical fibres and the size of the cell.

Transverse fibres, curved, differentating density The cells with this typology of fibres are causing local deformation, proportional to the density of fibres and the size of the cell. These cells make the global geometry flexible along the longitudal axis.

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4.3 GLOBAL AGGREGATION

GLOBAL AGGREGATION

3 1 2

CONNECTION BETWEEN PANELS

3 3 4

5 5 6

1

7

FLEXIBLE AREA

5 8 9

3 10 11

3 12 13

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DENSITY

STIFFNESS UNDULATION

DENSITY

4.3 GLOBAL AGGREGATION In the process of translating the experiments’ results into a selfsupporting physical system, we invented a representational setup based on the “vocabulary” of structural components as shown before (regional parameters).

Furthermore we developed a set of rules which we used to maximize our control over the final three dimensional result. The diagram shown on the opposite page was used as a bluepint, as an assembly manual and as a graphical way to prescribe in a two dimensional plan the resulted three dimensional surface.

Moreover, the panels were staggered in order to prevent a weak lognitudal seam along the structure. The vertical, lognitudal fibers that are running through the whole structure are parallel to each other and they have changing density, which controls the global curvature on the axis perpendicular to their direction.

Another important rule that is illustrated on this diagram is that the “+” typology is used where the one panel is meeting the next, because the “+” condition produces regionaly relatively stiff and flat areas, which make the connection to the next panel easier. The “-” indicate the areas that The global structure was panelized; are going to be more flexible and the each panel consisted of a different “|” symbolize the areas where the amount of stripes (1,3,5) and resulted undulation on the surface each stripe was made of a unique provides stability and stiffness. combination of the given elements (+, -, |). The numbers on the left of each panel indicate the amount of stripes 33

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5.0 CONCLUSION

CONCLUSION In this work a material system that follows organization principles found in natural systems was proposed and develop schematically at tablesize scale. The system proposed demonstrates the possibility of using material properties and geometrical patterns to generate a three-dimensional continuous surface with variable states of stiffness.

By setting parametric relations and changing these relations locally within the framework of an established set of rules, regions across the surface become stiffer or more flexible addressing different mechanical requirements. The regions of the surface in which these differences appear can be controlled according to geometric operations established in the design logic. While many design options were explored for the generation of various patterns, only one strategy with clearly defined parameters was selected to construct the final model. The system consists of two sets of fibers (curves) arranged perpendicular to each other. These fibers (curves) are bundled to form three defined grouping types which serve particular functions in the system. No special joints connections or transitional zones are required to connect these regions since all transitions are gradual changes within the order of the fibers. The system was reduced to a few parameters in order to gain a better understanding of the outcome in a

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state which could be better controlled. This does not exclude the possibility of further development of the system by combining other organization principles that were only explored in early experiments but not developed extensively. Despite our choice for reducing the number of parameters included for the final approach, the resulting three dimensional geometries achieved are far from being simple and impossible to be described in the two-dimensional planar projections of traditional architectural notation (plan and section). The resulting geometries exhibit both local and global double curvature with slight variations in curvature degree across the entire surface proving that basic geometric operations at a local level can guide the interaction between the constituent parts and lead to a complex outcome at a global level. The design approach presented in this work also demonstrates that material properties can be used in a more productive way than they are typically used in conventional construction systems.

The system proposed takes the most advantage out of the materials used by establishing an organization order in accordance with their physical properties.

FURTHER DEVELOPMENT The material system developed suggests the possibility of a design approach that could be scaled-up for architectural applications. The fabrication process can be scaled since there are fabrication tecniques available that can be used to produce the fiber patterns at other scales. In this project, the fabrication process employed for the production of the prototype relied on laser cutting technology for thin polypropylene sheets and the use of thin latex sheets as a base membrane. In the case of the fiber patterns, the fabrication limitation is posed by the size of the laser bed as well as the ability of the laser to cut thicker material sheets.

To operate at a larger scale two options may be explored. One path suggests continuing with the use of substractive manufacturing and replace the current technique with CNC milling. A second path suggests the fabrication of the fibers with an additive manufactoring technique such as 3D printing now available with the use of robotic arms and custom end-effectors. However, the main question to be solved is the choice of material. One must remember that the scalability of a schema or a diagram does not correlate to the scalability of material behaviour.

Material properties do not scale in the same way that geometry does. As mathematical or geometrical relations are not subjected to the physical laws

of the world because they are intrinsically ideal.

Material, on the other hand, is intrinsically real and as such it obeys the physical laws of the world.

Therefore, in the further development of this project our investingation will seek to establish a material choice for the fabrication of the fiber patterns as well as finding a base membrane with the elastic capacity to act on the fiber material selected.

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