Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2012
Nonlinear Finite Element Modeling of Prosthetic Lower Limbs Fadi A. Ghaith1, Fahad A. Khan2 Heriot Watt University/Department of Mechanical Engineering, Dubai, UAE 1 Email: firstname.lastname@example.org 2 Email: email@example.com
prosthetics in the past decades. A mono-limb model was developed by Lee et al.  using Abaqus for different three shank designs while the interaction between the limb and socket during walking was considered. The von Misses stress distributions in mono-limbs with different shank designs at different walking phases were reported and the possible failure modes were predicted. The results showed that the peak stress applied to the limb was lowered as the shank stiffness decreased. Finite element analysis for the evaluation of structural behaviour of the Sure-flex prosthetic foot and other loadbearing components was conducted by Omasta et al. . Detailed approach for the finite element modeling which includes foot analysis, reverse engineering and material property testing was provided. The foot analysis incorporated ground reaction forces measurement, motion analysis and strain gauge analysis. For the material model determination, non-destructive laboratory testing accompanied with FE simulation was used. Based on the obtained results, it was concluded that the fatigue failure was the most common component failure in the lower limb prosthetics. Falsig, et al.  developed a three-dimensional FE analysis to calculate stresses in a distal tibia. The bone was modeled as a composite structure consisting of cortical and trabecular bone in which the trabecular bone was either homogeneous with a constant modulus of elasticity or heterogenous with experimentally determined heterogeneity. The results were sensitive to variations in trabecular bone material property distributions, with lower stresses being calculated in the heterogeneous model. In the present work, a reliable computer model with appropriate assumptions and realistic conditions has been developed for a prosthetic lower limb that can withstand real loads at standing and jumping modes of operations. The developed model took into account the nonlinearity due to impact loading and the nonlinearity associated with contact analysis between the ankle and the foot.
Abstractâ€” In this study, three dimensional Finite Element (FE) modeling of prosthetic lower limb was performed for both titanium grade 5 and 302 stainless steel models with appropriate assumptions and realistic boundary and loading conditions. The developed model took into account many aspects of nonlinearity represented by contact surfaces and impact loading. The adopted design was selected carefully in order to match high strength and minimum weight criteria. Two types of FE analyses were performed; static analysis at standing position and dynamic analysis at jumping condition. The obtained results showed that the dynamic impact load is the most dominant since both materials were capable to stand with static load with minor Von Mises stresses acting on the pin connections. On the other hand, high Von Mises stresses were developed in the case of dynamic impact load which reached 590.8 MPa for titanium model and 831.6 MPa for stainless steel model. The obtained values of stresses are beyond the yield strength of titanium and exceed the ultimate tensile strength of stainless steel and causing failure. Index Termsâ€” Nonlinear Finite element, Prosthetic lower limb, Impact load.
I. INTRODUCTION Prosthetic limbs are incredibly valuable to amputees because prosthesis can help in restoring some of the lost capabilities with the amputated limb. Prosthetic lower limb consists of ankle joint and the foot. In order to make a highly efficient artificial limb, it should be provided that each and every component of the limb must function at high performance under several types of loading, particularly, impact loading. One of the important key factors in the design and fabrication of lower limb prosthesis is the type of material used in construction which plays dominant role in increasing the strength and lowering the overall weight of prosthesis. Many studies showed that carbon fiber, titanium and steel are preferred for the fabrication of mono-limb, joint and the inner foot structure . On the other hand, previous research suggested that many amputees prefer energy storing and releasing model (ESAR) using flexible shanks rather than the conventional solid ankle cushioned heel (SACH) feet on normal and fast walking [2,3]. In spite of that structural test specifications of lower limb prosthesis are specified in ISO 10328 , but performing such a test is found to be expensive and time consuming .Accordingly, computational analysis using FE software has been used widely in designing lower limb ÂŠ 2012 AMAE DOI: 02.ARMED.2012.2. 3
II. METHODOLOGY Finite element modelling of prosthetic lower limb has many sources of nonlinearity due to the impact load and the contact between the ankle and foot. Accordingly, ABAQUS 6.1/CAE software was selected using Dynamic/ Explicit Step mode to perform such complex analysis. The adopted methodology starts from selecting the proper design (i.e. geometry) and 1
Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2012 material of construction which satisfy both high strength of the component and minimum weight. This followed by conducting nonlinear FE analysis under dynamic loading (i.e. jumping condition) and static analysis (i.e. standing condition). III. FINITE ELEMENT MODELING This section describes the detailed steps of modeling the lower limb prosthesis within ABAQUS environment. A. Material Selection One of the important key factors in the design and fabrication of lower limb prosthesis is the type of material used for the construction. Since this work deals only with the prosthetic ankle and the foot structure, two types of materials were considered; Steel and Titanium. The mechanical properties being applied to the model are listed in Table 1. TABLE I. MATERIAL PROPERTIES Fig 1. Geometry of the monolimb and the pin.
B. Design The developed design was modeled initially by three separate parts such that monolimb represents one part, foot and flange consist the second part and the pin is the last part. The monolimb is designed as a 6mm hollow cylindrical rod attached to a surface. The outer diameter of the monolimb is 0.048m followed with the inner diameter of 0.036m. The monolimb is attached to a flange with a pin. The Pin diameter is 0.015m and its extruded from the flange surface to 0.05m. The monolimb and the pin were assembled as shown in Fig. 1. The foot is basically designed along with a holed flange as a single part. The geometry of the foot is shown in Fig. 2. The hole in the flange is introduced by the use of extrude cut option in Abaqus 6.1. The hole has a diameter of 0.015m and a length of 0.05m. The height of the part is 0.185m. The whole designed parts were assembled into one lower foot prosthetic model as shown in Fig. 3 while the floor was considered in the model for the purpose of impact analysis. Since the weight is a dominant design factor, it is important to mention that the overall weight of the modeled titanium lower prosthetic limb is 4.24 kg while it is 7.71 kg for steel lower limb.
Fig. 2. Geometry of the foot and flange.
Fig 3. Model assembly of prosthetic lower limb.
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Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2012 C. Interaction properties of the model In this analysis, the only interaction used was ‘General Contact (Explicit)’ interaction. This interaction takes place at the time of impact, between the foot and the floor and the between the ankle and the foot. D. Constraints Boundary conditions Two types of constraints were incorporated in the lower limb model; Tie constraint and Coupling constraint. Tie constraint was used to fix flange and foot as one single part and coupling constraint was implemented to restrict the motion of the foot to be only in the y-direction, towards the floor. The boundary condition of the floor was selected to be ‘Encastre’. This condition implies that both translational and rotational movements are prevented in all three dimensions.
Fig 4. Von Mises stresses acting on the foot of titanium Grade 5 model due to the impact load.
E. Loading and mass assignment The average mass considered in this study is 40 kg (a divided mass on one leg of 80 kg human being), the average height that a human being can jump up to is assumed to be 30 cm.Using this data, the velocity just before the contact between the model and floor was calculated. The time period of the step was altered in such a way that the simulation will take place until the foot has an impact with the floor. Gravitational load was assigned to the whole model in the ydirection towards the floor. A predefined load was assigned to the foot to be the velocity of the foot just before impact with the floor, which was estimated to be 2.43 m/s based on assumed jump of 30 cm.
Fig 5. Von Mises stresses acting on the pin of titanium grade 5 model due to the impact load.
The results obtained from the dynamic load analysis of 302 Stainless Steel model are shown in Fig 5 and 6. The maximum Von Mises stresses were found to be 831.6 MPa on the foot due to the direct impact with the floor. However, the yield strength of a 302 Stainless Steel is 651 MPa. This signifies that the model is under failure mode as it is exposed not only to plastic deformation but also reach fracture mode as it exceeded the ultimate strength. Apart from this, the developed stresses on the pin didn’t exceed 124.3 MPa. In order to assure that the impact load is the most dominant loading condition; additional runs were carried out under the influence of static loading due to the weight (i.e. simulating standing position). Fig.8 shows that the maximum Von Mises stress was found to be 26.6 MPa for 302 stainless steel model, while it is only 15.07 MPa for titanium model as shown in Fig. 9. It is important to recognize that maximum stresses acted on the pin connections in case of static loading. Taking into consideration the results obtained in the all cases mentioned above, it was observed that the titanium model was not only lighter than the stainless steel, but stronger as well. However, the difference in mass of both of the materials is found around 45%. Also it was observed that titanium model experienced lower stresses than the 302 stainless steel model under the same loading conditions. From another point of view, since the titanium model found to be lighter and stronger, this gives an opportunity to adapt more modifications; such reducing the mass or applying additional loads than those being applied in the current analysis.
F. Mode of failure Since the lower limb prosthetic model should not accept any kind of permanent deformation, the failure criteria was selected to be the yield strength of the material. IV. RESULTS AND DISCUSSION Numerical analysis was carried out for the FE model established in the previous section in order to predict the Von Mises stresses under the influence of both static and impact loading for Titanium and Steel models. It is important to mention that the mesh with total number of elements of 664938 was used to run the simulation as it satisfied the convergence criteria. Fig. 4 shows Von Mises stresses of the foot and flange under the impact load for titanium grade 5 model and Fig. 5 shows the stresses developed on the pin. Based on the obtained stress contours, it was found that the maximum stress during this analysis was 590.8 MPa, which was acting on the foot, whereas the pin stresses where comparatively very low. However, considering the yield strength for titanium which is 880 MPa, it can be stated that the model is a successfully designed as it stays in the elastic region. This also signifies that the model can adapt higher dynamic load.
© 2012 AMAE DOI: 02.ARMED.2012.2. 3
Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2012 CONCLUSIONS In this study, a prosthetic lower leg model was designed which consisted of the parts; monolimb, ankle and the foot. Two materials were selected for the model; Titanium Grade 5 and 302 Stainless Steel. The established design was chosen carefully to satisfy both criteria; strength and minimum weight. The model was designed successfully with overall masses of 4.24 kg and 7.71 kg for titanium and Stainless Steel, respectively. The developed model took into account many types of nonlinearities associated with contact surfaces and impact load. The selected mesh was successfully converged at a Global seed size of 0.002 and total number of elements of 664938. Both materials used in the model were found successful against Static Load Analysis. Titanium Grade 5 exhibited a maximum stress value of 15.1 MPa and 302 Stainless Steel exhibited a value of 26.6 MPa, which were acting on the pin connection. Both values are strongly below their yield strength, arising opportunities modify and improvise the model further more. For the Dynamic model, it was observed that the Titanium model exhibited some good results compared to Stainless Steel. The stress in the Titanium model reached a maximum of 590.8 MPa, giving flexibility for more modifications and reduction of weight. On the other hand 302 Stainless Steel Model fractured at a stress of 831.6 MPa.
Fig. 6. Von Mises stresses acting on the foot of 302 stainless steel model due to the impact load.
Fig. 7. Von Mises stresses acting on the pin of 302 stainless steel model due to the impact load.
REFERENCES  Jack E. Uellendahl, Prosthetic Primer: Materials Used in Prosthetics Part I , Amputee Coalition Organization (1998).http:// www.amputee- coalition.org/inmotion/ sep_oct_98 /matinprs.html.  Macfarlane, P.A., Nielsen, D.H., Shurr, D.G., Meier, K.,Perception of walking difficulty by below knee amputees using a conventional foot versus the Flex Foot. J. Prosthet. Orthot. 3 (1991), 114–119.  Menard, M.R. and Murray, D.D., Subjective and objective analysis of an energy-storing prosthetic foot. J. Prosthet. Orthot. 1(1989) 220–230.  ISO10328. Prosthetics––structural testing of lower limb prostheses. International Organization for Standardization, Geneva, 1996.  Lee W. C. and zhang M., Design of monolimb using finite element modeling and statistics-based Taguchi method. Clinical Biomechanics 20 (2005) 759-766.  Lee W. C., Zhang M., Boone D. A., and Contayonnis B., The effect of monolimb flexibility on structural strength and interaction between residual limb and prosthetic socket. Journal of Rehabilitation Research & Development 41(2004), 775786.  Omasta M., Palousek, D., Navrat T. and Rosicky J., Finite element analysis for the evaluation of the structural behaviour, of a prosthesis for trans-tibial amputees, Medical Engineering & Physics 34 (2012) 38– 45.  Falsig J., Hvid MD, and Jensen N., Finite element stress analysis of some ankle joint prostheses, Clinical Biomechanics 1(1986) 71–76.
Fig. 8. Von Mises stresses acting on 302 stainless steel model due to static load.
Fig 9. Von Mises stresses acting on Titanium Grade 5 model due to static load.
© 2012 AMAE DOI: 02.ARMED.2012.2. 3