LIBRARY MIchIgan State University PLACE ll RETURN BOX to move Ihb Mun M your mead. To AVOID FINES mum on or baton dd. duo. DATE DUE DATE DUE DATE DUE - ‘ r I i E j l C D J! l l. MSUIoAnAfflmuIvkom/E O - Initiation (pal ppommny ”3-9.1 MEASURING AND MODELING FORCE-DEFLECTION RESPONSES OF HUMAN THIGHS IN SEATED POSTURES BY Bing Deng A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Material Science and Mechanics 1 994 ABSTRACT MEASURING AND MODELING FORCE-DEFLECTION RESPONSES OF HUMAN THIGHS IN SEATED POSTURES By Bing Deng There is great interest in automotive seat comfort. Physiological factors that affect seating comfort are related to deformations and forces within people's bodies and their seats. Deformability of soft tissues is a significant determinant of body-seat interface contours along the back of the thigh. This thesis describes the measurements of the mechanical responses of the hamstring regions of seated human subjects. A seating fixture with load cells and electronic gauges was built to support people in a variety of seated postures that affect the length of and the tension in the hamstring muscles. While pushing a flat, rigid surface into the back of peoples‘ thighs, force-time and displacement- time data were collected and analyzed. Two-dimensional, plane strain, finite element models were developed to represent the thigh compression responses. Models were created with geometries that were specific to each often subjects, ranging from small female to large male. The properties of the in vivo soft tissue were assumed to be isotropic, homogeneous, and hyperelastic. The same material characteristics were used for all subjects. Comparisons between computational responses and experimental measurements showed close agreement. It is concluded that the finite element method presented in this thesis is useful in soft tissue modeling and is an effective quantitative tool which may be used for seat cushion design. DEDICATION To my parents and my brother for their support. To my husband for his love and encouragement. ACKNOWLEDGMENTS The author would like to extend her heartfelt gratitude to the following very special people, for their assistance and expertise. To my co-workers and friends, for their help and the happiness I enjoyed with them during my study at Michigan State University: Cathy Boomus, Robert Boughner, Neil Bush, Tamara Bush, Mark Mazzulo, Frank Mills, and Melissa Sloan. To Clifford Beckett for his help from repairing glasses to developing 'the seating fixture used for the experimental measurements. To Johnson Controls Inc. for their generous funding of this project. To Dr. Larry Seglind for his kindness and valuable advice in the development of the finite element models. To Dr. Renold Averill and Dr. Roger Haut for reviewing my work and serving on my committee. To my graduate advisor: Dr. Robert P. Hubbard. Thank you for your friendship and guidance on everything I have set out to do. IV TABLE OF CONTENTS Bane LIST OF TABLES LIST OF FIGURES CHAPTER 1. BACKGROUND AND OBJECTIVES 1 CHAPTER 2. LITERATURE REVIEW 9 CHAPTER 3. FINITE ELEMENT METHOD ' 23 Geometry 23 Material Properties 30 Boundary Conditions 32 Finite Element Formulation 33 Computer Method 36 CHAPTER 4. EXPERIMENTAL METHODS 38 CHAPTER 5. RESULTS AND DISCUSSION 54 Experimental Results I 54 Finite Element Results 69 Experimental Measurements and Model Results Comparison 76 CHAPTER 6. CONCLUSION AND FUTURE WORK 89 REFERENCES 91 APPENDICES A. ABAQUS Program ' 94 B. Consent Form for the Non-invasive Measurement of Deformations and Loads in the Human Thighs of Seated Postures 105 C. Protocol for the Non-invasive Measurement of Deformations and Loads in the Human Thighs of Seated Postures 107 D. The standard error calculation between experimental and computational results 1 10 Table 2-1. Table 2-2. Table 3-1. Table 4-1. Table 4-2. Table 4-3. Table 4-4. Table 5-1. LIST OF TABLES Material Properties of Bulk Muscular Tissue under Compression [15] Material Properties Used in the Below-Knee Study [16] Cylindrical Femur Dimensions Subject Physical Data Subject Anthropometric Measurements Thigh Circumference for Human Subjects [7] Thigh Measurements Standard Error between Computational and Experimental Results VI 1 9 20 27 43 45 46 47 78 LIST OF FIGURES EinuLe. 1-1. 2-D models of the small female, average male, and large male 1-2. JOHN 2-D motion with TLC=10° to 40°, TRA=35° and HRA=o° 1-3. 3-D skeletal model 1-4. The musculature of the buttocks and legs represented as ellipsoids 1-5. JOHN model with skin contour 2-1 Chow and Odell's axisymmetric finite element model of buttock [10] . 2—2. Results of buttock model on a flat frictionless rigid surface [10] 2-3. Comparison of load-deflection plots from the testing of a physical model and the finite element model [10] 2-4. The axisymmetric finite element mesh of Brunski et al. [12] 2-5. The loading fixture and testing results of Sacks et al. [14] 2-6. Deflection-force response of Vannah and Childress' study [18] 3-1. Posterior muscles of the right thigh [20] 3-2. Cross section through the middle third of the left thigh seen from below [20] 3-3. Standard higher order, biquadratic element [21] 3-4. 2-D, plane strain finite element model 4—1 The seating fixture used for experimental measurements 4-2. The load cells used for force data collection VII 11 12 13 15 17 22 25 26 28 29 39 41 4-4. 4-5. 4-6. 4-7. 4-8. The instrument for measurements of force and deformation under the thigh The testing setup for the experimental measurements Thigh compression test for the time history of force under the buttock Thigh compression test for the time history of force on the back of the pelvis Thigh compression test for the time history of thigh deformation Thigh compression test for the time history of force under the thigh Experimental measurements of three trials at the same knee angle Experimental measurements of previous three trials and retest two trials for one subject at the same knee angle Experimental measurements under different knee angles for subject 1 Experimental measurements under different knee angles for subject 2 Experimental measurements under different knee angles for subject 3 ' Experimental measurements under different knee angles for subject 4 Experimental measurements under different knee angles for subject 5 VIII 42 49 50 51 52 53 56 57 59 60 61 62 63 5-10. 5-11. 5-12. 5-13. 5-14. 5-15. 5-16. 5-17. 5-18. 5-19. 5-20. 5-21 . 5-22. Experimental measurements under different knee angles for subject 6 Experimental measurements under different knee angles for subject 7 Experimental measurements under different knee angles for subject 8 Experimental measurements under different knee angles for subject 9 Experimental measurements under different knee angles for subject 10 The undefonned and deformed grid of the model The principal stress distribution in the lateral direction The principal stress distribution in the vertical direction The principal stress distribution in the out of plane direction Von Mises stress distribution The shear stress distribution Computational results and experimental measurements comparison for subject 1 Computational results and experimental measurements comparison for subject 2 Computational results and experimental measurements comparison for subject 3 Computational results and experimental measurements comparison for subject 4 IX 64 65 66 67 68 70 71 72 73 74 75 79 80 81 82 5-23. 5-24. 5-25. 5-26. 5-27. 5-28. Computational results and experimental measurements comparison for subject 5 Computational results and experimental measurements comparison for subject 6 ' Computational results and experimental measurements comparison for subject 7 Computational results and experimental measurements comparison for subject 8 Computational results and experimental measurements comparison for subject 9 Computational results and experimental measurements comparison for subject 10 83 84 85 86 87 88 CHAPTER 1 BACKGROUND AND OBJECTIVES As customer expectations rise, automotive seat comfort is becoming an increasingly important design goal. Seating comfort and discomfort are the biological responses of people to their seating environment. Comfort is related to positions, motions, forces, and deformations within people and their seats. The basis for a comfortable seat is that the seat contour fits people and allows them to change to a position that is compatible with the geometry of their bodies and their movements. New biomechanical seat design tools, which provided quantitative information about positions and motions, have been developed by previous work [1]. These models accurately represent the geometry and movement of different size people in seated postures. Side view, 2-dimensional computer models of the small female, average male, and large male are shown in Figure 1-1. The positions and motions of the torso skeletal structures for different amounts of lumbar curvature have been studied and represented. These models represent the human body with three rigid segments, the skull, rib cage, and pelvis.” The rigid segments were connected by two flexible links, the cervical and lumbar spines. The work done by Has [2] determined that the movements of the rib cage relative to the pelvis due to lumbar spinal movement can be represented as an even distribution of the total rotation at each of the lumbar joint centers and no rotation in the thoracic region. Figure 1-2 illustrates the 2-D model motions as presented by Has. This result provided a way to specify the placement of the thorax relative to the pelvis depending on lumbar curvature. The assumption of uniform distribution of vertebral motions has been verified by the recent study of Cao, et al. [3]. J“ M! 5! «an (ml. 50‘ out: In. I» can: In. FIGURE 1-1: 2-D models of the small female, average male. and large male. ' LC=10° to 40°, TRA=35° and HRA=0°. Boughner [4] developed JOHN 3-dimensional computer model of the 50th percentile adult male skeleton. The skull geometry was based on the study of Hubbard and Mcleod [5, 6]. The geometry for the rib cage and limbs was based on the appropriate landmark locations in the human anthropometric study performed by the University of Michigan Transportation Institute (UM-TRI) [7]. The pelvic geometry was from the work of Reynolds, et al. [8]. The JOHN 3-D model is shown in Figure 1-3. The torso of the 3-D model articulates in the same way as the 2-D models. In addition to modeling the 3-D skeleton, Boughner analyzed different methods of modeling muscle shapes and hamstring muscle length. Boughner [4] used the simple geometric shapes of ellipsoids to represent the musculature of the buttocks and legs, as shown in Figure 1-4. The guteal, quadriceps, hamstring, and calf muscles are each represented with a single ellipsoid. Since the soft tissues under the buttocks and thighs are easy to deform when contacting with a seat surface, these contours will change significantly under seating pressures. Bush [9] continued the work on the JOHN 3-D skeletal model of the average man. The vertebral column and back muscles were added to the 3—D computer model to define the contours of the thoracic region. A skin was also generated on the back side of the JOHN model torso (Figure 1-5). The external contours on the back side of the torso can be used to design seat contours. The 3—dimensional model of the skeleton, major muscle groups, and back contours represents the possible postures of the human torso in a way that is useful in seating lay-out and design. The deformation of the soft tissues on the back of the rib cage are relatively small compared to the soft tissues under the thigh. While the external body shapes along the back of the torso are determined primarily by the positions of skeleton and overlying structures, the external body contours along FIGURE 1-3: 3-D skeletal model. \~ . Gutcal » Quadriccps muscle \ muscle Hamstring ., muscle Calf muscle FIGURE 1-4: The musculature of the buttocks and legs represented as ellipsoids. FIGURE 1-5: JOHN model with skin contour. the back of the thigh are a function of soft tissue deformations in addition to skeletal position. Deformability of soft tissues is significant to body-seat interface along the back of the thigh. Representation of soft tissue responses with computer modeling is an important step toward tools for seat designs that will comfortably accommodate people. The goal of this study is to measure and model the mechanical responses of human thighs in seated postures that are significant to body-seat interaction. More specifically the objectives of this thesis are to : (1) Measure the force-deflection responses of human thighs in a variety of seated postures that affect the length of and tension in the hamstring muscle. (2) Develop finite element models to represent the force-deflection responses of the hamstring muscles using UNIX-based finite element programs. (3) Compare the computational force-deflection responses with the experimental measurements to verify the accuracy of the finite element models. , This thesis is strucrtured into three sections: one devoted to the 2-D finite element model development, the second devoted to the experimental measurements using the specially designed testing chair, the third devoted to the comparison between model results and experimental measurements. The force versus deflection responses of the back of the human thighs are studied both from experimental data and finite element model results. CHAPTER 2 LITERATURE REVIEW A project titled as "Measuring and Modeling Force-Deflection Responses of Human Thighs in Seated Postures" involves the fields of biomechanics, anatomy, elasticity, and finite element method. Both engineering and clinical literature should be considered. Although considerable work has been done with respect to the modeling of some human tissues, few attempts have been made to model thigh tissues and their effect 'on seating. The soft tissues in the thighs consist of the following anatomical components: bone, muscle, subcutaneous fat, and skin. The largest component of soft tissue in the thighs is muscle. Very little work has been done to determine the material properties of in vivo bulk muscle in compression. Some significant literature related to bulk soft tissue study is discussed below as a reference for this thesis research. Using finite element method, Chow and Odell [10] studied the deformations and stresses in the buttocks due to various surface pressure loading. An axisymmetric, three dimensional finite element model of a human buttock was created. This model simulated a position with no thigh contact, which gave a nearly axisymmetrical pressure distribution. Thirty-three 12-node, curved, isoparametric quadrilateral elements were used. Figure 2-1 showed the cross-sectional layout. The model was composed of a 100 mm radius hemisphere of soft tissues with a rigid core to represent the ischial tuberosity. Soft tissues did not slide along or move away from the rigid core and were assumed to be linear, elastic, and isotropic. The initial Young's modulus was 15,000 Pa, based on the true stress and strain measurements of synthetic gels. A Poisson's ratio of 0.49 was chosen. Such Poisson's ratio caused less than 3.5 10 percent volumetric shrinkage under hydrostatic pressure. A smaller Poisson's ratio of 0.47 gave 10.5 percent decrease in volume which was unrealistic for body tissues. Chow and Odell's study was based on a body weight of 779 N and a hip width of 400 mm. A vertical force of 300 N (38.5 percent of the body weight) was applied to the model through the cushion-buttock interface. A linear elastic incremental method was used to deal with large deformations. The internal three dimensional stress state was from six different loading conditions: floating on water, floating on mercury, sitting on a rigid frictionless flat surface, applying a modified cosine pressure distribution, sitting on a foam cushion (with friction), and sitting on a foam cushion with lubricated interface. For sitting on a flat frictionless rigid surface, the load was applied with an increment of 9 N. The initial stiffness was very small. As the contact region increased, the load to deflection ratio increased. In order to not have the thickness of the soft tissues at the tip of the penetrator compressed to zero, when the loading reached 122 N, the Young's modulus was increased to a ”very large" value of 30,000 Pa. The finite element result was checked against the testing of a physical model, a hemisphere constructed of wood for the ischial tuberosity and gel for soft tissues. Figure 2-2 and Figure 2-3 show the resulting stresses and a comparison for the load-deflection relationship. The comparison for load-deflection relation showed that the model result was more compliant than the testing- result. The authors also discussed the accuracy of the finite element method. The normal and shear stress at the boundary were checked against the applied pressure and shear. The integrated value of vertical component of the surface stress should be equal to a vertical load of 300 N and was controlled to within 11 RIGID CORE ELEMENT \ . )2 I 50 mm 25m IOOmm T 25mm II 21 3| 3' 10 9 28 a 19 9 7 IB ' e ELEMENT I7 25 NUMBER 6 22 53531 3 0' 6‘1 ‘1 4 2 3 ,3 '6 \NODAL CODE 7 :I-l 5 FIGURE 2-1: Chow and Odell‘s axisymmetric finite element model of buttock [10]. 12 3000 m (I D :2 2000‘» m c: a .1 1000] g IAI ‘5 400 z 0 RADIUS FIGURE 2-2: Results of buttock model on a flat frictionless rigid surface. (a) Surface pressure distribution, (b) Final grid pattern, (c) Von Mises stress contour, (d) Hydrostatic stress contour [10]. IN MM DEFLECTION 13 E- 0.3 \ FINITE ELEMENT E-o.0I5 - .. ...--— " " ' ’EXPERIMENT DEFLECTION INITIAL “To T I00 200 300 LOAD IN NEWTONS FIGURE 2-3: Comparision of load-deflection plots from the testing of a physical model and the finite element model [10]. 14 one percent. The authors concluded that the finite element method was useful to simulate the deformations and stresses in soft tissues. Reddy et al. [11] developed a simple 2-dimensional model of buttock cushion interactions. An experimental buttock model from a semi-circular slab of PVC gel (13.9 cm in diameter and 3.8 cm thick) was tested under uniaxial compression. The soft tissue of the buttock was assumed to be represented by the gel. It was determined experimentally that the gel material could be described adequately by the neo-Hookean form of strain energy function, w, where w=c(l,-3) (2-1) where c is a material constant and was found to be 3 KPa. I1 is the first strain invariant. . Four different foam cushions and a PVC gel cushion, each 38 mm thick, were studied under a vertical load of 20.2 N acting on the buttock. The stress distributions developed in the buttock model were compared among different cushions. Theoretically, all biological tissues were described as being nonlinear, anisotropic, and viscoelastic. The authors discussed the qualitative differences between the soft tissues of the buttocks and the PVC gel model, but they did not show that the model was a reasonable approximation for buttock modeling. Brunski et al. [12] produced pressure sores in laboratory pigs using a constant force pneumatic indenting system. Anatomic regions for the indentations were slightly lateral to the mid-thoracic portion of the spine. Rigid cylindrical indenters with same shaft diameter but different surface radii of curvature (8 cm and 3 cm) were used. An axisymmetric finite element model, ./,\/ \. / / /\/\ /\ XIII /\/‘\ 3 1 /\/\/\/\/\/\/\//\l/\ /\_/\/\ K \/\/.\/ /\//V/\ \ /l\ / I I l J4- FIGURE 2-4: The axisymmetric finite element mesh of Brunski et al. [12]. 16 with higher-order linear strain triangle elements, comprised of two layers, one layer of skin, and the other of fat and muscle, with thickness ratio of 1 to 10. The mesh is shown in Figure 2-4. These layers were assumed to be attached to one another. The tissue was assumed to be linear, elastic, and isotropic. The Young's modulus, taken from the literature, for skin layer and fat/muscle layer were 2.76 MPa, and 0.162 MPa, respectively. Poisson's ratio for both materials was 0.49, a common value used for nearly incompressible materials. The value for fat/muscle was originally determined from Yamada's study of the tensile properties of panniculus adiposus from several pigs [13]. lndentations were made up to 10% of the total thickness of the model. Results of the finite element analysis were compared for two different indentors. Some qualitative comparison was made between the animal experiments and the results of the finite element simulation. Sores developed in a circular area of about the same size as the predicted contact area of the flatter indenter. For the rounder indenter. sores developed in a smaller area directly beneath the indenter. The authors felt that their model would serve as a useful starting point for future work. Sacks and co-workers [14] used an indention mechanism to measure, in vivo, the static stiffness of the soft tissue of the proximal femur in side-lying subjects, two paraplegic and two without disabilities. A simple technique of making marks on the shaft that supported the load was used to measure the skin displacement beneath the indentor. Measurements were taken immediately after each load was applied. The testing fixture and obtained average pressure- displacement relations are shown in Figure 2-5. It was found experimentally that the diameter of the femur was essentially constant for all subjects. The stiffness of the tissues under compression increased with age, regardless of disability. But no quantitative data was reported for soft tissue stiffness. STRBE'T Attachment to fixed table >. Displacement Marks 6) U T lndentor. 25- Age 0 AS 62 A H0 34 1‘}: 20* Cl JS 49 .,- O JST 51 .5}. if: 15~ (L 0 01 e 3’ 10— < ‘O .92 ‘s 5 < o l l l 1 _l 4 8 12 16 20 Displacement, mm FIGURE 2-5: The loading fixture and testing results of Sacks et al. [14]. 18 Krouskop and others [15] devised a gated Doppler ultrasonic motion sensing system for making non-invasive measurements of the bulk soft tissue properties, in vivo. Six subjects were tested on the forearm or leg. The system consisted of a holding jig to support the limb that was being tested, a tissue vibrator, and an ultrasonic transducer to monitor the motion of the tissue. Using a 10 Hz mechanical oscillator (much like an indentor) to excite the tissue, the resulting tissue motion was measured by ultrasound. The ultrasonic transducer was controlled by an external computer to control the depth at which the sensor was measuring tissue displacement. The collected data composed of the initial strain imposed on the tissue, the amplitude of the mechanical vibration, the frequency of the vibration, the depth of the scatterer being interrogated, and the magnitude of the motion of the scatterer. Then the modulus of the tissue was calculated using the following equation [15] : __ 2 U2(Xa—X1) _ E—zrw Ur-U2_U2"Ua (2 2) Xz-XI Xs-Xz where u. corresponded to the motion amplitude at the point corresponding to the depth x., w was the frequency of the cyclic displacement, and r was the density of the soft tissue. ' The modulus obtained from ultrasonic experiment were verified by testing the tissue at the same position using an lnstron Testing Machine. Force- displacement data were collected and the modulus of the tissue was calculated. The comparison showed a very close agreement. Table 2-1 summarized the reported tissue properties, given as an elastic modulus in KPa at 10% strain. 19 Table 2—1. Material Properties of Bulk Muscular Tissue under Compression [15] Contraction State Young's Modulus (KPa) relaxed 6.2 mild isometric contraction 36 maximum isometric contraction 109 Steege and coworkers [16, 17] investigated the use of finite element analysis in the below-knee socket design. The first approach was to attempt to match the interface pressures measured from experiments with the pressures predicted via a three-dimensional finite element analysis. The finite element model consisted of soft tissue, cartilage, bone, and socket liner. The shape of the residual limb came from multiple transverse Computer Assisted Tomography (CAT) scans. The CAT scan images were digitized by hand, and data were built into a mesh of linear elements. A plunger device consisted of a small load cell and an LVDT was attached to the socket with seven holes to measure the property of the soft tissue. During stance, the plunger was depressed through the ports and into the tissue. The Young's modulus was calculated from the outputs load-displacement curves of two subjects. The modeled tissue was given an initial guess value for E. Then, an average value of Young's modulus was obtained by comparing the ratio of finite element analysis and experimental displacements at the holes to the initial E value. The material values used in the finite element model are shown in Table 2-2. 20 Table 2-2. Material Property Used in the Below-Knee Socket Study [16] Material Yougq's Modulus (KPa) Poisson's Ratio Bone 1. 55x106 0.28 Soft Tissue 6.00 0.49 Cartilage 79.00 0.49 This finite element analysis was based on linear, small-strain elastic assumptions. The model had predicted the range of experimental interface pressure measurements with reasonable accuracy (0 to 12 KPa). However, the calculated and experimental pressure at any particular point did not match well. Due to the lack of one to one correspondence between the modeling and experimental technique, further work had commenced [17, 18]. Several modifications to the previous finite element model were performed. The bony elements were represented as a rigid body. A finer mesh was employed around areas where high pressure gradients were expected. The element type of soft tissue were changed to incompressible, non-linear isoparametric with large displacement capability. MARC, a general purpose finite element code was used for the analysis. The incompressible isoparametric elements allow representation of material as an elastomer, a polymer with incompressible, low stiffness behavior. The Mooney-Rivlin strain energy function, w, was chosen to specify the material properties: W = C10 (I1 - 3) + C01 ('2 " 3) (2'3) where I1&I2 were strain invariants, 010 and 001 were material constants which 21 can be obtained experimentally. For this study, C10 and cm were approximated by a reasonable assumptions for elastomers: Co1= 0.25 C10 and E = 6(010 + Cm) (2'4) However, the values of the material constants were not mentioned in their paper. The large strain incompressible model results were similar to the previous linear model. At the time this paper was published, this model was still being developed. The authors felt that the finite element technique had excellent potential for prediction of the mechanics at the limb/socket interface for below- knee amputees [17]. Vannah and Childress [18] did a series of indentor tests on the calf area of a non disabled human subject to determine the static mechanics of bulk muscular tissue for limb/socket study. An LVDT and load cell was used to measure the imposed deflection and the resulting resistive force. Isometric force leveled up to 20% of body weight. Typical deflection-force curves were shown in Figure 2-6. The curves were repeatable. The results showed nearly linear force-deflection curves with a significant amount of hysteresis for small deformations. Stress relaxation occurred only within the first second after deflection application. The experiment which applied displacement in a stepwise manner rather than applied continuously seemed to result in a more non-linear deflection- force relationship. Repeatability of the displacement-force curves and lack of continuing stress relaxation were both surprising results [18]. 22 8- . El spacer1-in 0 spacer2-in 6- u spacer3-in a u 2 s 4- " E a p 2-1 a O e an o-e ‘ . . . , a 0 10 20 Displacement (mm) 3 .. D spacer1 - in 0 spacer 2 - in 5 - :1 spacer 3 - in n 0 spacer 3 - out n g 0 :34 ~ 3 Le 53 I o a 2 ~ 3 ° 0 . e do 0 ¢ . V I I I —1 0 1 0 2 0 Displacement (mm) FIGURE 2-6: Deflection-force response of Vannah and Childress' study [18]. CHAPTER 3 FINITE ELEMENT METHOD Finite element methods are numerical procedures for solving physical problems with differential equations or energy theorems [19]. The method is easily applied to irregular-shaped objects composed of several different materials and having mixed boundary conditions, where exact solutions are usually not available. This method involves a discretization of a continuous structure into a number of sub regions (elements). An approximation equation in terms of the unknown nodal values is written for each element, then the system of equations are assembled using standard techniques. The resulting equations are then solved, yielding the structural response. A finite element model consists of a geometric description, which is given by the elements and nodes, and a set of mechanical properties associated with the elements. These properties include material characteristics and parameters for interface elements. Boundary conditions are imposed throughout the analysis. Using general computer programs, the finite element analysis process requires the input of: (1) geometry, (2) material properties, (3) boundary conditions. Geometric: The soft tissues in the thighs consist of the following anatomical components: bone, muscle, fat, and skin. The geometry of the internal biological tissues are complicated. The largest component of soft tissue in the thighs is muscle. The posterior muscles of the thigh are the semitendinosus, the biceps femoris, the semimembranosus, and the posterior part of the adductor magnus, as shown in Figure 3-1 [20]. All these muscles, except the short head of the 23 24 biceps, arise from the ischial tuberosity, and all except the adductor magnus cross the knee joint. As these muscles are traced downward from their origin on the ischial tuberosity, they separate, some distance above the knee, into medial and lateral ones [20]. Boughner [4] studied different methods of modeling muscle shapes and used the simple geometric shapes of ellipsoids to represent the musculature of the thighs in the JOHN 3-D model (shown in Figure 1-4). For finite element modeling in the present study, an idealized model was chosen which consisted of a circular cylindrical hamstring muscle component with a tubular femur on the top. A cross-section through the middle third of the thigh was cut to illustrate the general anatomy of the thigh, as shown in Figure 3- 2 [20]. The approximate ratio of diameter of femur to hamstring muscle is 0.4. The dimensions of hamstring muscles were based on the experimental measurements of the human subjects' thigh circumference at mid-shaft and the distance from the bottom of thigh to a straight line between the greater trochanter and the lateral condyle of the femur. Treating the cross-section of the thigh as an idealized circle, the diameter of the hamstring muscles could be calculated from the thigh circumference measurement. An average value of hamstring diameter calculated from the thigh circumference and the distance from the bottom of thigh to the mid-line was taken as the geometric data to describe the hamstring muscles in the finite element models. The average calculated value was used as the diameter of the circular muscles. Sacks and co-workers [14] found experimentally that, for transverse loading of the proximal femur in side-lying postures, the diameter of femur is essentially constant for all of their subjects. Three-dimensional model of the skeleton, major muscles, and torso contours for the average male has been developed in previous work [1]. Small female and large male models are under development in the current work. These three model sizes are based on the 25 I / / (I lschiol ____ tuberosity __/, 7' 1'“T ‘ Sciolic n. — 7%“ '. .. Adduclori ,,, ,,' ‘ ‘5 A. r I I ' ‘ I l~ " ’ 7‘ 5,]. I- ;‘ . ‘ . .' - f \ O o I I. If“ 8 I“ ' Trbrol n. - I ‘ ‘ r . . Common U} W . — -' _ fl ' l' . \‘ ‘ "A: It; . 1 '1 . ’ a. " I 0‘ n ' r peroneol n. FIGURE 3-1: Posterior muscles of the right thigh [20]. 26 Vaslus medialis Medial inlermuscular seplurn Fascia over adduclor canal t Reclus Iemoris I .' laleral Iemoral culaneous n. femur Saphenous n. ‘/ Sariorius ./ my. / g.‘ :’\\¢ ; ‘I 5/ \ Femoral v. and (1. ~. /./) , ’ Anlerior Iemorai/< 3?:de // flit/:5 ’ v . culaneous a“)... I ‘3‘ ,. w. Adduclor Iongus» .2 sapIrenous v. / .- fi’” Deedeemoral . m ’07/ ,.///y//,,/ a. on v. '/ .1 ' 7’7???) Anlerior bronchi ”(Wl/ / /¢ .’ , oi obluralor 11.'\' ‘W‘ ,/ "/77.” ,. .. .. Gracilis "\"\ /_' /’ .135}, ,x .. Adduclorwfl, we? ' 39' n". " ' magnus . / \ o Fascia Iala "'\ Perforating vessels \\ I /-f T \. -w o "g“- Semilendinosus Poslerior Iemoral culancous n. *7, '2 I”: . O .. .' o , . . . i ' l ' ‘ II .‘ , Voslus " iniermedius \ ------ Vaslus ' IaleraIis /"' IIiolibiaI Irocf ------ laleraI inlermuscular seplurn Biceps, long head FIGURE 3-2: Cross section through the middle third of the left thigh seen from below [20]. 27 anthropometricidimensions of UM-TRI [7] study. The femur is represented as a circular cylinder in the 3-D models. According to the dimension of femur in these models, the radii of femur for small female, average male, and large male are 16 mm, 17 mm, and 21 mm, respectively. Using the approximate ratio of 0.4 for diameter of femur to hamstring muscles, the radii of femur were calculated from the dimension of the hamstring muscles. These calculated femur diameter showed a very close agreement to the three human models size. The ranges of values used in the finite element models of different size subjects for femur radii are given in Table 3-1: Table 3-1. Cylindrical Femur Dimensions Subjects Large male Average male Small female Femur radius The circular cylindrical model of the hamstring muscles consisted of 302 eight-node, biquadratic, reduced integration, plane strain elements. This standard isoparametric element is shown in Figure 3-3. The element type are nearly incompressible, non-linear isoparametric with large deformation capability. A uniform mesh was generated in half of the cross-section due to the symmetry of the model. The use of higher order elements in this case resulted in retaining the numerical accuracy in the finite element analysis. Hybrid elements were primarily intended for use with the almost incompressible material behavior of soft tissues. Reduced integration uses a lower-order integration to form the element stiffness. Reduced integration usually provides more accurate results (provided the elements are not distorted), and significantly reduces computation 28 1 5 2 8 - NODE ELEMENT FIGURE 3-3: Standard higher order, biquadratic element [21]. time [21]. The femur was represented as a rigid cylinder and the testing surface was a rigid flat plate. Thirty planar interface elements were used along the boundary of soft tissues to simulate the contact interactions between the deformable soft tissues and rigid femur and test surface. Each interface element had three nodes that were shared with the surface of the deformable mesh, and a ”rigid body reference node”. The degrees of freedom at this node defined the motion of the rigid body. A mesh containing 1519 nodes and 302 elements with 2644 variables is shown in Figure 3-4. The diameters of soft tissue and femur were based on each subject measurements. The model geometries were specific to each subject. 29 P““““‘ Flliflflflflflfiflflflfl nihiiih unniiiiiii FIGURE 3-4: 2-D, plane strain finite element model. 30 Miss: One of the most important steps in modeling biological tissues is to determine the appropriate material properties. Soft tissues of the thigh are very complex. The anatomical components that exist in the thigh include bone, muscle, fat and skin. Each of these distinctive layers present unique material properties. In reality, all biological tissues are nonlinear, anisotropic, and viscoelastic. They also contain blood vessels, lymphatics, nerves and interstitial fluids. In this stage of analysis, the skin, fat, and muscle were modeled as a single soft tissue beneath the hard tissue of the femur. The soft tissue was modeled as a homogeneous, isotropic, and hyperelastic material. A number of soft tissue studies have been discussed in the literature review. It was found that little work has been done to measure the mechanical properties of bulk muscular tissue of human thighs in vivo. Chow and Odell [10] used the Young's modulus and Poisson's ratio of 15 KPa and 0.49, respectively, to model the soft tissues of human buttock. The material parameters were based on the measurements of a synthetic gel model. The ischial tuberosity was modeled as a rigid core. Roddy et al. [11] described the material behavior of a physical human buttock model by the neo-Hookean form of strain energy function (shown in 2-1). The material constant, c, was found to be 3 KPa by testing the gel material under uniaxial compression. Brunski and coworkers [12] took the Young's modulus of fat and muscle as 162 KPa from literature, which was originally determined from the study of the tensile properties of panniculus adiposus from pigs [13]. Krouskop and others [15] made non-invasive measurements of the bulk soft tissue properties on the forearm and leg, in vivo. The modulus obtained at ten percent strain for relaxed bulk soft tissues was 6.2 KPa. 31 Steege et al. [17] developed a finite element model for the below-knee socket design. The initial elastic modulus was 6 KPa for soft tissue. The Mooney-Rivlin strain energy function was chosen to specify the material properties. The two material constants were related by the assumption: Co1=o.25C1o (3'1) However, they did not mention the value of cm in their study. This thesis study was based on the assumptions that the soft tissues of the thigh can be considered homogeneous, isotropic, and elastic. In all of the elasticity models, the hyperelasticity models are the only models that give realistic predictions of actual material behavior at large elastic strains [21]. The soft tissue of the thigh was modeled to be an approximately incompressible isotropic elastomer. The material was described in the polynomial form of strain energy potentials [21]: U=cloIII-3)+Co1(l2-3)+g1-(Ja4)2 13-2) where U is the strain energy per unit of reference volume, cm. co, and D1 are material parameters, 1, and 12 are the first and second deviatoric strain invariants. J... is the mechanical elastic volume ratio. For this study, cm: 0, cm = 1.43 KPa, and D, = 0.014 1/KPa. The initial Young's modulus and Poisson's ratio were 8.52 KPa and 0.49, respectively [11,15,16,17,18]. Based on the values taken from the literature, it was expected that the material parameters used in this thesis study were appropriate for soft tissue modeling. Using these material characteristics, the model results showed 32 close agreement with the experimental measurements. Same values were used to model the mechanical responses of human thighs for all subjects with model geometries that were specific to each individual. Win05: There are two choices to reduce a three-dimensional problem to a two- dimensional problem: plane stress and plane strain. The model assumption of plane strain was used. Plane strain is a specialization of 3-dimensional linear elastic theory. It occurs in the case that the dimension of the body is very large and is not free to move in the direction perpendicular to the plane of the applied loads. If we assume that the applied loads lie in the X-Y plane, then w, the displacement in the Z-direction, is zero. The displacements in the X and Y direction, u and v, respectively, are functions of only x and y. This set of displacements makes the strains of en. 9x21 and 9,,z each zero. The plane strain problem reduces to the determination of a... a”, and 0., as functions of x, y, only [19]. Due to the symmetry of the problem, only half of the cross-section of the hamstring region of the thigh was modeled. The left edge of the model was the line of bilateral symmetry. The nodes along this line were constrained from horizontal movement. The model was characterized by large deformations and contact. The reference node of the femur was fixed. No motion was allowed for the bone. Prescribed displacements on the rigid flat plate were used in the loading. The plate was displaced vertically up into the hamstring muscles. The specified displacement acting on the rigid flat plate was considered to be applied in increments. Smooth contact and rough frictional contact were both assumed in 33 the models. However, no significant influence on the force-deflection relations was found. W Analytical methods in structural analysis have been studied for many years. Exact solutions are usually not available for problems with complicated geometry and/or boundary conditions. A commonly used numerical technique for structural analysis is the finite element method. Applications of the finite element method to solid mechanics involve the theory of elasticity. First,'a relationship is developed between strain and nodal displacement. The displacement anywhere within an element, u, can be approximated by polynomials expressed in terms of the displacements at the nodes, {u}: u=IN1 {u} ' 13-3) where [N] is the matrix of the element shape functions which depend on the element type. The strain components are then related to the element displacements u. The solution of problems in the classical elasticity theory are generally obtained by assuming infinitesimal deformation. The strain is evaluated by considering only the first order terms in the displacement gradient; the second order terms are neglected. Soft body tissues are easily deformable but practically incompressible. The materials are capable of experiencing large deformation before any type of failure occurs. Both first order and second order terms must be taken into consideration during large deformation. The large 34 change in geometry produces a non-linearity in strain-displacement relation. The strain-displacement relation in matrix form is [22]: ' 35 l(_a_u+gv_)‘ “(292423): auau+avaf E": 8x 2 8y 8:: +_1_ 8x 81: 8x8); 8x8); (3_4) " 191$) a 2 amaze (i)(§z) L28y8x ay - [axay axay ay ay_ The total strain can be divided into infinitesimal strain and large strain components. Equation (3-4) can be written as [23]: £1,- = eij +11],- (3'5) The infinitesimal strain in matrix form is: {e} = [Bo]{u} (3-6) The large displacement component for plane strain in matrix form is: {n} = [Ba]{u} (3-7) The subscript G is used to denote the geometric matrix which is a function of the displacements. The strain-displacement relation becomes [23]: {8}= [Bo]{u}+[Ba]{u} (3'3) 35 By combining the infinitesimal and geometric parts, the strain can be related to the nodal displacements by the nonlinear operator: {e}= {Bria} 13-9) where [B] = [Bo] + [Be]- The stress and elastic strain components are related by the generalized Hooke's law as [19]: {c}=lDl{e} (3-10) The coefficients in [D] for plane strain are [19]: ' 1-7 1 1—27 1-27 E 1- lDl=1+ 7 i 7 1—27 1-27 0 0 O (3-11) NIH C where E is the elastic modulus, y is the Poisson's ratio. The element stiffness matrix and the element force vector are the element's contribution to the system of equations that result when the potential energy is minimized. The potential energy consists of the strain in the system minus the work- done by the forces acting on the system. The strain energy in a two-dimensional elastic body is [19]: A=-;-j(onen+o,,e,,+o.,e.,)dV (3'12) V Equation (3-12) can be written in terms of the element nodal displacements as: 36 A=§IuITIKIIuI (343) where [K] is the elemental stiffness matrix defined by equation (3-14): [Kl=][BJ’ID]IBIdv 13-14) The work done by the concentrated forces is the {u}’{P} product. The total potential energy in a continuous two-dimensional elastic system is [19]: II: :A—{u}’{P} (3-15) where n is the total number of elements. Then, the potential energy is minimized, yielding the system response. QanuifiLMflthd: In previous work, the three-dimensional human model was developed using SDRC-IDEAS software [24], a commonly used program for modeling and analysis. Initially, the finite element models were attempted in IDEAS version VI. Unfortunately, IDEAS version VI do not have the capability to solve problems with large deformation and/or large strain characteristics. A general purpose finite element program, ABAQUS [21], was selected for the calculations and pre- and post-processing. ABAQUS is developed by Hibbitt, Karisson and Sorensen, Inc., which allows for non-linearity in both geometry and material properties, viscoelasticity, incompressible and nearly incompressible materials. This code also has a wealth capability for interface elements to model contact problems. 37 The ABAQUS input file for one subject is listed in Appendix A; it contains geometric descriptions, material properties, and boundary conditions, and it was written using standard ABAQUS commands. The programs were then executed on a SUN SPARC 690MP. The total load per unit length of the cylindrical hamstring muscles was obtained by the reaction force on the rigid plate reference node. The lateral displacement was obtained by the horizontal movement on the most outside node. The vertical displacement versus force and the vertical displacement versus lateral displacement served as the analytical results for comparison with responses measured with the thighs of the human subjects. CHAPTER 4 EXPERIMENTAL METHODS Deformability of soft tissues is a significant determinant of body-seat interface contours along the back of the thighs. Measuring and modeling force- deflection responses of human thighs in seated postures are important steps for seat designs. Testing is also the best method to verify the results of any analytical techniques. ' The experiment that was developed to determine the force—deflection characteristics of hamstring muscles of human thighs made use of a specially designed chair that supports a person in a variety of seated postures that affect the length of and the tension in the hamstring muscles on the back of the thigh. The seating fixture is shown in Figure 4-1. The chair is constructed by Unistrut connected with various fittings. This seating fixture provided a backrest, a pelvis support, and a movable footrest to change knee angle from 90 to 180 degrees. The knee angle is defined as the angle between two vectors: one from the femur greater trochanter to the lateral condyle of femur, another from the lateral condyle of femur to the lateral malleolus. The backrest and pelvis support both have pivot points that allow rotation about lateral axes to comfortably accommodate subjects. The dimensions of the chair can be adjusted to correspond to each individual's body size. A shaped wooden backrest was connected to the Unistrut chair by two angle fittings which served as pivots. The backrest can be adjusted both vertically and horizontally. The backrest supports a person's torso in the rib cage region. A 12 X 5 inch plastic plate supports the back of the pelvis and a load cell was attached to the plate to measure the force on the back of pelvis. 38 39 FIGURE 4-1: The seating fixture used for experimental measurements. 40 Two pieces of 4.5 inches square plastic plate were used to support the right and left buttocks with a half inch gap between them. There was a small hole in the middle of each plate to position the iscial tuberosities. A load cell was put under each plate to measure the force under the buttocks. These three load cells are ultra precision fatigue rated load cells, shown in Figure 4-2 (A). The output is 2 mv/v. The strain gage type is bonded foil [25]. The range of measurements is 500 pounds. A16 X 11 inch aluminum plate was fixed on the Unistrut to provide mama. . A hydraulic jack with 2 ton capacity and 5 inch stroke capability was positioned on two pieces of Unistrut under the right thigh. A testing surface could be moved upward by the jack to compress the thigh. The position of the jack could be adjusted in three directions. A electronic depth gauge provided measurements of thigh deformation. A pipe clamp connected the gauge to the jack with a small aluminum plate, so the movement of the jack could be read through the gauge. The linear accuracy of the gauge is :l:0.001 inch. The range is 0-6 inch (0-150 mm). Two load cells were attached to the jack with an aluminum plate to measure the force under the thigh. The load cells positioned side by side laterally 80 mm from the center line of the jack. These two load cells are precision miniature load cells with 500 pounds available range, shown in Figure 4-2 (B) [25]. A small bar was put on the top of two load cells to position a flat, plastic surface ( 10 X 5.5 inch) that was slowly raised to contact and load the hamstring muscles. This stiff, plastic plate was the testing surface. It could rotate about a lateral axis to align with the back of the thigh. This instrument is shown in Figure 4-3. Ten normal volunteers with different thigh circumferences were tested. The physical characteristics of the subjects are listed in Table 4-1. The age ranged from 21 to 50 years, the height ranged from 62 to 75 inch, and the weight I "H" _ .3. -"oo' I "I" :1] [ CLEARANCE FOR - E‘ "N” "1:" scnews ELECTRICAL CONNECTOR i hi BENDIX PIN PCOZA-‘IO-SP MATING CONNECTOR: BENDIX PIN PCOGA-I 0—68 (A). Ultra precision fatigue rated load cell [25] 3!. WRENCH FLAT (B): Precision miniature load cell [25]. FIGURE 4-2: The load cells used for force data collection 42 r I. r» i = . 1' . .3 FIGURE 4-3: The instrument for measurements of force and deformation under the thigh. 43 ranged from 97 to 215 pounds. Table 4-1. Subject Physical Data Subject No. Gender Hmanch) WeLtLhtjb.) Again/ears) 1 Male 73 1 90 5O 2 Male 67 1 30 25 3 Male 70 1 95 34 4 Male 75 21 5 29 5 Female 68 1 1 8 22 6 Female 67 . 125 26 7 Female 66 160 21 8 Male 71 1 55 25 9 Female 62 97 25 1 0 Male 71 1 57 47 Written informed consent was obtained from each subject prior to testing. The consent form used in this project is attached in Appendix B. To remove clothing as a variable, all subjects were shorts during testing. Prior to the thigh compression testing, some anthropometric measurements were taken with the subjects in erect standing postures. These measurements include: (1) Hip Width: the distance between the right and left Anterior Superior lliac Spine (ASIS). (2) Hip to Knee Length: the distance between the femur Greater Trochanter and Lateral Condyle of femur. (3) Knee to Foot Length: the distance between the Lateral Condyle of femur Thesr 44 and the Lateral Malleolus. (4) Log length: the distance from bottom of foot (without shoes) to knee pivot. (5) Hip Angle: Subject lies prone (stomach down) on a flat, horizontal surface so that the right and left ASIS and the pubic symphsis is in contact with the flat surface. Place a 5" by 12" flat board across the ”flat" part of the upper rear of the pelvis, across the sacral region at the level of the right and left Posterior Superior Iliac Spine (PSIS), and measure the angle of this board relative to the horizontal surface with an angle finder. This is the angle between anatomical definition of hip angle and measurements of hip angle. These basic measurements are summarized in Table 4-2 45 Table 4-2. Subject Anthropometric Measurements Subject Hip Width Hip Angle Hip-to Knee-to- Leg Length No. (mm) (degrees) Knee Foot (mm) Length Length (mm) (mm) 1 279 20 41 9 41 9 501 2 267 1 5 381 394 464 3 242 20 394 445 520 4 279 20 470 470 572 5 203 1 9 41 9 41 9 495 6 246 1 5 432 381 470 7 241 1 7 400 432 483 8 21 6 20 .394 445 520 9 228 1 2 362 356 41 3 10 254 5 41 9 394 500 After the chair had been adjusted according to each subject's body size, the subject sat in this seating fixture, feet placed firmly on the footrest plate, head and body in a relaxed posture with the hands dropped to the sides of the chair. The circumference of the right thigh was measured using a steel tape in a plane perpendicular to the long axis of the thigh at mid-shaft. The thigh side-to- side width and thigh anterior-to-posterior thickness were also measured with a caliper. An extensive study on human anthropometry in automotive seats has been completed by the UM-TRI [7]. They measured the middle circumference of 46 the thigh in a relaxed driving posture. The measurements for the 50th and 95th percentile adult male and the 5th percentile female are summarized in Table 4-3: Table 4-3. Thigh Circumference for Human Subjects [7] Subjects Minimum (mm) Maximum (mm) Mean (mm) Large male 485 635 559 Average male 442 550 504 Small female 370 - 472 427 Based on the data of UM-TRI study, the subjects in this project were divided into small female(S.F.), average male(A.M.) and large male(L.M.) according to the thigh circumference. The results are given in Table 4-4. The measurements of thigh are also listed in Table 4-4. 47 Table 4-4. Thigh Measurements Subjects Thigh Thigh Side-to- Thigh Group No. Circumference Side Width Ante rior-to Definition (mm) (mm) Posterior Thickness (mm) 1 584 1 68 1 88 L.M. 2 470 1 43 1 60 A. M. 3 534 162 . 21o L.M. 4 670 1 86 225 L.M. 5 483 1 32 1 64 A.F. 6 505 1 50 1 81 A.F. 7 540 1 60 1 80 LP. 8 480 1 36 1 72 AM. 9 425 1 22 1 4O S.F. 1 O 485 140 1 71 AM. mm the leg muscle relaxed, the testing surface was slowly raised to contact with the hamstring region of the right thigh. As the testing surface was raised further, the force between the back of the thigh and the testing surface was measured by the two load cells under the testing plate. The deformation of the thigh in the vertical direction was measured by the gauge attached to the hydraulic jack. The deformation of the thigh in the lateral direction was measured by another electronic depth gauge, which was operated by the investigator. The testing surface was raised in steps of about 3 mm, the force 48 and deformation data were collected after a ten second wait to allow for force relaxation and to approach a quasi-static condition. The tests were performed for different knee angles at 90, 120, 150, and 165 degrees. There were three trials for each knee angle. A typical testing setup is shown in Figure 4-4. The protocol of the measurements is attached in Appendix C. Force-time and displacement-time data was collected on an IBM compatible personal computer equipped with an analog to digital conversion board and an amplifier. A Quick Basic program was used to control the data acquisition. The program prompted the user to enter the file name, to save the data, and to take a set of samples. Typical force-time and displacement-time data for one subject are shown in Figures 4—5 through 4-8. All the data are processed using Microsoft Excel. The vertical displacement versus force and the vertical displacement versus lateral displacement relations served as the experimental results that were compared with the finite element model results. 49 FIGURE 4-4: The testing setup for the experimental measurements. 50 28:3 65 one: 85.. .6 8.52 we: 65 .9 .59. 8.99650 8.5 ”m4 wane: 0mm 82m 8:8: 588 SE III 32... 85 xeofim 5.. 693 2:2. mum oow mi 03 www 2: mm on mm o _ b p _ _ — — u _ I l l r 1 1 10 o l0 0 N In N I 02. 1 mm? E N) naming out repun 9910:] mhw O O N ( i mNN 1 0mm 51 .328 05 Co x000 9.: co 090.— »0 >55: OE: 9.: 5.. 82 95.885500 :02... ”01v $59.”. omN AoomVoEF mg 08 mm F on F mm? cow mu om mm o .1 _. n w 4 u E a u z o l m I .8 l we .1 cm 1. mm f on r mm I 8 (N) swear euI Io me 6111 no 9010.4 52 .cozopEouou :95 no 205.: OE: 05 .0» +3.. CQQQQEOO :95 "in szGE com 53230 .993 IIOII cannozoo .mo_to> 89$ 08:. mt om? m9 9.: mm on mm a _ qr— - ‘ 8 8 8 ° ° N 1— (ww) uorreuuoreo IIBILII O 0 O [\ 53 5.5 9: boa: 86.. .6 22%. we: we. 6.. 59 5.89668 :95 84 8502 om? CS 03. p m 0.0... b _ 68¢ 08:. 2: om _ b — — o o. 8 8 m: m 8 m m cm m 8 .u. m. 2. w 8 m 8 8. o: CHAPTER 5 RESULTS AND DISCUSSION The goal of this study is to measure the mechanical responses of human thighs in seated postures and develop finite element models for analysis and simulation. Ten normal subjects with different thigh circumferences were tested. The sizes of the subject's ranged from small female to large male. A constant displacement increment of 3 mm was applied to the posterior region of the right thigh. Force-time and displacement-time data were collected after a ten second wait to allow for force relaxation. ExperimentaLLesults: Before the results .of the finite element models are presented, the data from the experiment will be discussed. Force-time and displacement-time plots for one subject are shown in Figure 4-5 through 4-8. The force on the back of the pelvis appeared nearly constant in the testing period. The small fluctuation in the data is due to subject motion. The force under the buttock of the tested side decreased as the force, deformation of the thigh increased. The force under the buttock of the free side did not change significantly. The force under the tested thigh increased non-linearly with time. The deformation of the thigh in the vertical direction increased linearly with time and the deformation of the thigh in the lateral direction increased non-linearly in the time period. Force-time and deflection-time data of the thigh were processed and analyzed to study the mechanical responses of human thighs in seated postures. The relation of vertical displacement versus force reflects the stiffness of the soft tissues in the thigh. The vertical displacement versus lateral displacement 54 55 relation reflects the geometry change of the thigh. These two relationships served as the experimental results for comparison with the analysis. The relationship between vertical displacement and force began linearly and became stiffer as the contact region increased. This is a typical force- displacement relationship for soft tissues under compression with increasing contact area [10, 18]. All the subjects were tested at different knee angles and three trials were performed for each knee angle. Two plots cf vertical displacement versus force and vertical displacement versus lateral displacement for a typical subject are shown in Figure 51. One of the subjects was tested again after two months. The thigh circumference did not change for this subject and the loading was applied to the same region of the thigh. The testing results are shown in Figure 5-2. There were three trials for the previous test, and two trials for the retest. The data are consistent for the previous measurements and retesting results. The soft tissues under the thigh showed repeatable deformation-force behavior and geometry change under same testing condition. The test repeatability was shown by consecutive testing for all the subjects and retest on one subject two month later. The plots were nearly identical for three trials at the same knee angle for each subject. Preconditioning of soft tissues to obtain repeatable results does not appear to be necessary for in vivo test [18]. 56 5o .. E ,0 .. 30 .. 20 .. g 10 -- E 0 ' : : : 1 : : : 0 lo 20 30 40 50 60 70 Vertical displacement (mm) —9— Trial 3 —’— Trial 2 —*— Trial 1 (A) 0 IO 20 30 40 50 60 70 Vertical dsplacement (mm) —9—— Trlal 3 —’— Trial 2 -—*—- Trial l (3) FIGURE 5-1. Experimental measurements of three trials at the same knee angle. 57 es 0) O A U Lateral Dlsplacernent (mm) 3 '5’ 0 10 20 30 40 50 60 70 Vertical Displacement (mm) —-A—— m2 —9— pre.1 + pm.3 «um —I— mm (A) d '0 0| d l r Force under the thigh (N) N OI so .. 25 - o : 0 10 20 30 40 50 60 70 Vertical Displacement (mm) reteett +reteet2 —9—pre.1 +prez +pre.3 (3) FIGURE 52 Experimental measurements of previous thress trials and retest two trials for one subject at the same knee angle. 58 The tests were performed at different knee angles: 90, 120, 150, and 165 degrees (except for subject 2 at 170 degrees and subject 6 at 175 degrees). The results for all knee angles of ten subjects are shown in Figure 5-3 through 5- 1 2. The measurements showed that the width of the thigh increased and the thickness of the thigh decreased as the knee angle increased. The vertical displacement versus lateral displacement relation (Figure 5-3 (A) through 512 (A) ) for most subjects showed that the lateral deformation of soft tissue of the thigh became smaller with knee angle increased, except for subject 6 and 7 the trends were not clear. The force-deformation relation (Figure 5-3 (B) through 5-12 (B) ) showed that the slopes of the curves increased as knee angle increased, which means that the soft tissues became stiffer as the knee straightened. These results indicate that the tension in the hamstring muscles of thigh increased as the knee straightened. However, the changes of the soft tissue stiffness were comparatively small in the normal driving postures (knee angle ranging from 120 to 150 degrees). 59 50 .. E ,0 .. 30 .. 20 .. g 10.. 3 0 1 1 1 1 1 1 1 0 I0 20 30 40 50 60 70 VOflIcaI dsplacernent (mm) KA90 + KAI20 KAISO —°'— KA'IbS (A) I50 1' 125 .. 1CD i 3 3 75 .1 50.. Q, 25 .. .-. H , 0 1‘ ‘1 4" 78"" 1 1 1 1 1 1 0 IO 20 30 40 50 60 70 Vertical dsplacernent (mm) KA90 '—‘—- KAI20 KAI50 “—0— KA165 (3) FIGURE 5-3. Experimental measurements under different knee angles for subject 1. 60 5o .. E ,0 .. 30 .. m .. 2 10 «- 3 0 - ~c- ~ 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Vertical dsplacementtmm) KA90 —*—' KAIZO KAISO —°'— KAI70 (A) 1w .- race (N) a: 9 0818 Vertical dsplacernenttmm) KAISO —'°_ KAI70 (3) FIGURE 54. Experimental measurements under different knee angles for subject 2. 61 50 .. E ,0 ._ 30 .. 20 . g ,0 .. E 0 e: 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Vertical clsplacernent (mm) KA90 ""'*—" KA120 KAISO —°_ KA165 (A) 0 10 20 30 40 50 60 70 Vertical displacement (mm) KA90 —""— KAIZO KAISO —°'— KA165 (3) FIGURE 5-5. Experimental measurements under different knee angles for subject 3. 63 w" E... 1... gm! g 10 ~- 3 0e -' 1 1 . 1 1 1 0 lO 20 30 40 50 60 Verticaldsplacementtmm) 70 KA90 —+’ KAI20 KAI50 —°—— KA165 (A) 0 IO 20 30 40 50 60 Vertical dsplacemenf (mm) KA90 —"— KAI20 KAISO —°— KAIbS (3) FIGURE 5-7. Experimental measurements under different knee angles for subject 5. 64 20 30 40 50 Vertical clsplacernent (mm) KA90 —*— KAI20 KAISO —°— KAI75 (A) I50 r 125 1- if!) g I ,, . 3 751 E 50 25 .. ,- .-. 0 1' *1 (in: P 1 1 1 1 1 1 0 l0 20 30 40 50 60 70 Vertical clsplacement (mm) KA90 —*'— KAI20 KAI50 —°— KAI75 (3) FIGURE 58. Experimental measurements under different knee angles for subject 6. 65 1111‘ 5 Laleraldispiacement (mm) 0 IO 20 30 40 50 60 70 Vertical displacement (run) KA90 -—*— KAI20 KAI50 —°— KA165 (A) 50 60 70 Vertical dsplacement (mm) KA90 —"—' KAI20 KAI50 —°_ KA165 (3) FIGURE 59. Experimental measurements under different knee angles for subject 7. 66 0 IO 20 30 40 50 60 70 Vertical dsplacement (mm) KA90 "_'*— KAI20 KAISO —°'_ KA165 (A) Force (N) Vertical dsplacernent (mm) KAISO —°— KAIbS (3) FIGURE 5-10. Experimental measurements under different knee angles for subject 8. 60 91111 d o l ‘ lderaldlsplacementtmm) 0 IO 20 30 40 50 60 70 Vertical dsplacement (mm) KA90 _*'— KAI20 KAISO —°— KAI70 (A) Vertical deplacernent (rnnt) KAISO —°— KAI70 (3) FIGURE 5-4. Experimental measurements under different knee angles for subject 2. 61 0 10 20 30 40 50 60 70 Vertical clsplacemenf (mm) KA90 _'*"— KAI20 KAI50 —°— KA165 (A) 0 IO 20 30 40 50 . 60 70 Vertical dspIacement (mm) KA90 _*—_ KAIZO KAI50 —°_ KAI65 (3) FIGURE 55. Experimental measurements under different knee angles for subject 3. 62 0 IO 20 30 .40 50 60 70 Vertical dsplacemenf (mm) KA90 "—*_ KAI20 KA150 —'°"— KA165 (A) 1- 0 IO 20 30 40 50 60 70 Vertical dsplacemenf (mm) KA90 —'*_ KAIZO KAISO —°— KA165 (3) FIGURE 56. Experimental measurements under different knee angles for subject 4. 63 0 lo 20 30 4O 50 60 70 Vertical dsplacement (mm) KA90 —"‘—' KAI20 KA150 —°— KAI65 (A) 150 r I25 1* 1m .. 3 g 75 50 .. 25 .. o - . : : 1 0 IO 20 30 40 50 60 70 VOI‘IIcaI dsplacernent (mm) KA90 —""_ KAI20 KA150 —°— KAIbS (3) FIGURE 5-7. Experimental measurements under different knee angles for subject 5. 64 O 10 2O 30 4O 50 60 70 Vertical dsplacernent (min) KA90 —*'_ KAIZO KAISO —°— KAI75 (A) 0 IO 20 30 40 50 60 70 Vertical clsplacement (mm) KA90 —*— KAI20 KAISO —°— KAI75 (3) FIGURE 58. Experimental measurements under different knee angles for subject 6. 65 0 IO 20 30 4O 50 60 70 Vertical displacement (mm) KA90 _'*'_ KAI20 KAISO —°— KA165 (A) 50 60 70 Vertical dsplacement (mm) KA90 "_‘— KAI20 KAISO “—9— KA165 (3) FIGURE 59. Experimental measurements under different knee angles for subject 7. 66 O 10 20 30 40 50 60 70 Vertical dsplacement (mm) KA90 —"‘_ KAI20 KAI50 —°'— KAI65 (A) Force (N) O 10 2O 30 4O 50 60 70 Vertical dsplacernent (mm) KA90 "'—‘_ KAI20 KAI50 —°—— KA165 (3) FIGURE 5-10. Experimental measurements under different knee angles for subject 8. 67 0 .. 1 1 1 1 1 1 0 10 20 30 40 50 60 7O VOI‘IICOI dsplacement (fl'l‘l't) KA9O —*— KAIZO KAISO —°'— KA165 (A) 0 l0 2O 30 4O 50 60 70 Vertical dsplacement (mm) KA90 —‘— KAI20 KAI50 —°_ KA165 (3) FIGURE 5-11. Experimental measurements under different knee angles for subject 9. 68 0 IO 20 30 4O 50 60 70 Vertical clsplacement (mm) KA90 —*'_ KAI20 KA150 ‘_°_ KAIbS (A) 150 '- 125- 2 100-1 i 3 75 + 1 .1 5, ._ 25 r w: e .i’fy 0 9' .1- 1 1 a 1 % . : 0 I0 20 30 4O 50 60 70 Vertical clisplocemenftm'n) KAISO —°—' KAI65 KA90 '—*—" KA120 (3) FIGURE 5-12. Experimental measurements under different knee angles for subject 10. 69 W: The finite element model was created using UNIX-based program ABAQUS [21]. The model was simplified to contain a deformable cylinder for the soft tissue, a rigid cylinder for the femur, and a rigid plane for the test surface. The soft tissues were modeled as a single homogeneous, isotropic and hyperelastic material. Prescribed displacement on the rigid flat plate was used as the loading. The plate was displaced vertically up into the hamstring muscles and very large deformation took place. The undeformed and deformed shapes of the model are shown in Figure 5-13. The total load per unit length of the soft tissue was obtained by the reaction force on the rigid plate reference node. The lateral displacement was obtained by the horizontal movement on the most outside node. The vertical displacement versus force and the vertical displacement versus lateral displacement served as the analytical results for comparison with responses measured with the thighs of the human subjects. The principal stresses, 011,022, and 033, calculated with the ABAQUS program are shown for one subject at 70 mm deformation of thigh in Figure 514 through 516. The initial diameter of hamstring muscles for this subject is 110 mm. The plots show the stress distributions in the soft tissue underthe femur. Von Mises stress and shear stress on are shown in Figure 5-17 and 5-18, respectively. The stress contour plots showed that the maximum value for each case occurred inside the soft tissue instead of the contact boundary. The models only contained a single set of material properties for the soft tissues in the thigh and the geometry of the soft tissue was idealized as a cylinder. However, the stress distributions obtained from the model predictions could serve as the analytical results to compare with the pressure measurements at the body-seat interface. The internal stress distributions may 70 a ,_= =a“~“ K”““‘ z.iii‘NNNM”4555—5:- , FIGURE 5-13: The undeformed and deformed grid of the model. 71 Maximum "alue = Minimum “alue = FIGURE 5-14: The principal stress distribution in the lateral direction. 72 Maximum "311.19 = 2.1“?6 at n‘xje ‘ l-linimum value = —1.581 at n::le I“ FIGURE 5-15: The principal stress distribution in the vertical direction. 73 Maximum “alue = Minimum ”alue = FIGURE 5-16: The principal stress distribution in the out of plane direction. 74 Maximum Value = Minimum '.'a1ue : I ISES TALUE ‘3 - :- FIGURE .5171 Von Mises stress distribution. Maximum Minimum ”alue ”alue 75 FIGURE 5-18: The shear stress distribution. 76 comfort. Further study of stress distribution that may be related to the seating comfort will continue. The relationships of vertical displacement versus force and vertical displacement versus lateral displacement for 90 degrees of knee angle were obtained both from experimental measurements and the finite element models. The purpose of comparing the model results with the experimental measurements is to show that the finite element models developed in this work can be used as a tool in seat cushion design. The plots for each subject are shown in Figures 5-19 through 5-28. The computational and experimental results of vertical displacement versus lateral displacement relation (Figure 5-19 (A) through 5-28 (A)) are almost identical for eight subjects (except for subject1 and 2). This indicates that, even though the representation of the soft tissues is much simpler than their anatomy, the models developed in this work provide very good predictions of actual geometry changes of human thighs interacting with a rigid surface. The vertical displacement versus force relation (Figure 5-19 (B) through 528 (B)) showed a fairly close agreement between the measured and modeled responses. For the vertical deformation ranging from 20 to 50 mm, the forces of the measurements are higher than the model results for most of the subjects. For the vertical deformation above 50 mm or by the end of testing, the forces of the measurements are lower than the model results for most of the subjects. The testing results showed a relatively more linear relationship between vertical displacement and force than the computer modeling results. The difference might come from the simple geometries and material properties used in the finite element model. All the soft tissues in the thigh are modeled as a single 77 homogeneous, isotropic and hyperelastic material. This is a simplification of the mechanical properties of bulk muscular tissues of human thighs in vivo. All biological tissues are typically nonlinear, anisotropic, and viscoelastic. The model only considered the hamstring region of human thighs interacting with the rigid surface. In the compression tests, the mechanical responses of human thighs are not only affected by the hamstring group but also by other groups of soft tissues, such as quadriceps group. The finite element models developed in this project provide a first step in using computational tools in body-seat interaction study. Model the complete structure of human thighs with detailed geometries and incorporate the viscoelastic characteristic into the model are suggested for future work. Standard error (see Appendix D) between experimental and computational results are calculated for each subject. The standard error for force and lateral displacement are summarized in Table 5-1. For vertical deformation of thigh ranging from 0 up to 75 mm, the standard error in force ranged from 8% to 27% (4 to 13 N); the standard error in lateral deformation ranged from 2% to 26% (0.6 to 7 mm). Although the representation of the soft tissues is much simpler than their anatomy, the comparison between experimental results and model prediction for all the subjects, ranging from small female to large male, indicate that the models developed in this work predict the thigh compression responses accurately. 78 Table 5-1. Standard error between computational and experimental results Subject No. SE. in force SE. in force Siffilglleaxerfii (Sji.SEF;liar;learr‘eer:tl (N) 1%) (mm) ‘°’°’ 1 9 20 7 26 2 9 24 5 23 3 4 9 3 1 2 4 4 1 O 1 4 5 4 8 1 A 8 6 7 1 7 4 1 4 7 8 1 3 1 13 8 1 3 27 2 1 1 9 9 23 0.6 2 1 O 1 0 27 3 1 4 79 50 .. E .. .. 30 .. 20 .. g 10 -» E 0 1 1 1 1 1 1 1 0 lo 20 30 40 5O 60 70 Vertical dsplacement (mm) TEST DATA —.—' MODEL RESULTS (A) I F 0 IO 20 30 40 50 60 70 Vertical dsplacernent (mm) TEST DATA —0— MODEL RESULTS (3) FIGURE 5-19. Computational results and experimental measurements comparison for subject 1. 8O w .. ‘E 5 40 ~- 30 1. m . g 10 1 0 1 1 1 1 1 1 4 0 IO 20 30 4O 5O 60 70 Vertical dsplacernent (mm) TEST DATA —.— MODEL RESULTS (A) o ' 10 20 30 49 50 so 70 Vertical dsplacerrtent (rnm) TEST DATA —0— MODEL RESULTS (3) FIGURE 5-20. Computational results and experimental measurements comparison for subject 2. 81 O 10 2O 3O 4O 50 60 70 Vertical dsplacernent (mm) TEST DATA + MODEL RESULTS (A) 0 IO 20 30 4O 50 60 70 Vertical dsplacernent (mm) TEST DATA —.'—" MODEL RESULTS (3) FIGURE 5-21. Computational results and experimental measurements comparison for subject 3. 82 . m .. E .0 .. 30 .. 20 .. g 10 -- E 0 1 1 1 . - 1 1 1 0 IO 20 30 4O 50 60 70 Vertical displacement (nun) TEST DATA -—0— MODEL RESULTS (A) 150 .. I25 - g it!) ~- 3 75 1 i? 50 .. 0 1 1 1 4 1 1 O 10 20 30 4O 50 60 70 Vertical dsplacement (mm) TEST DATA —'0— MODEL RESULTS (3) FIGURE 5-22. Computational results and experimental measurements comparison for subject 4. 83 50 .. E. .0 .. 30 .. 20 .. 5 10 - d 0 ' 1 1 1 1 1 1 fl O 10 2O 30 4O 50 60 70 Vertical dsplacernent (nun) TEST DATA —'.— MODEL RESULTS (A) I50 1' I25 1- A 1 n fir 1 I ' ' 0 IO 20 30 40 50 60 70 Vertical dsplacement (mm) TEST DATA —°'— MODEL RESULTS (3) FIGURE 5-23. Computational results and experimental measurements comparison for subject 5. 84 81382.6 d o 1 Y Lderdmplacernenltmm) O 0 lO 20 30 40 50 60 70 Vertical dsplacement (mm) TEST DATA '_.‘— MODEL RESULTS (A) L I l f 0 10 20 30 40 50 60 70 Verllcal dsplacemenl (mm) TEST DATA —0—- MODEL RESULTS (3) FIGURE 5-24. Computational results and experimental measurements comparison for subject 6. 85 m .. E 40 .. 30 .. m .. g 10 . E 0 1 1 1 1 .9 41 1 0 IO ' 20 30 40 50 60 70 Vertical dsplacemenl (mm) .TEST DATA —0— MODEL RESULTS (A) 1 fi 0 10 20 30 .40 50 60 70 Vertical dsplacement (mm) TEST DATA —0— MODEL RESULTS (3) FIGURE 5-25. Computational results and experimental measurements comparison for subject 7. 86 a) .. E 40 ._ 30 .1. 20 .. g 10 ~ 3 0 1 a 1 1 1 1 1 0 TO 20 30 40 50 60 70 Vertlcal dsplacement (mm) TEST DATA —°— MODEL RESULTS (A) 150 1' I l r r 0 10 20 30 40 50 60 70 Vertical asplacement (mm) TEST DATA —0— MODEL RESULTS (3) FIGURE 5-26. - Computational results and experimental measurements comparison for subject 8. 87 laierddlsplacemenflmm) 13 13 1 as 10 cu- 0 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Vertical dsplacement ("I“) TEST DATA —.— MODEL RESULTS (A) 150 1 1w .- 110 ‘- g 90 1- 8 70 a. E 50 w ._ 10 -*- 1 L l 1 1 l "0 10 20 30 40 so 60 7o Verllcal deplacement (mm) TEST DATA —.— MODEL RESULTS (3) FIGURE 5-27. Computational results and experimental measurements comparison for subject 9. 88 50 1. E 40 .. 30 .. 20 .. g 10 ~- 3 0 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Vertical dspiacernent (mm) TEST DATA —’— MODEL RESULTS (A) A 0 10 20 30 40 50 60 70 Vertical displacement (mm) —.— MODEL RESULTS TEST DATA (3) FIGURE 5-28. Computational results and experimental measurements comparison for subject 10. ‘ CHAPTER 6 CONCLUSIONS AND FUTURE WORK The objectives of this thesis are to measure the force-deflection responses of human thighs, to develop finite element models to represent the thigh compression responses, and to compare the computational and experimental results. The three specific objectives investigated for this work have been accomplished. The mechanical responses of human thighs in a variety of seated postures have been measured on ten human subjects, ranging in thigh size from small female to large male. Repeatable results have been obtained for the same seating posture. Tests were performed at different knee angles: 90, 120, 150, and 165 degrees. As the knee straightened, the stiffness in the soft tissues of the thigh increased. The measurements provide useful information about the defomrability of soft tissues along the body-seat interface. Two-dimensional, plane strain, finite element models have been developed to represent the thigh compression responses of the hamstring region. The soft tissues were modeled as a single homogeneous, isotropic, and hyperelastic material. The same material properties were used for all size subjects with model geometries that were specific to each subject. The relations of vertical displacement versus lateral displacement and vertical displacement versus force served as the testing and modeled results. Comparisons between the measured and modeled responses for the hamstring region of 90 degrees knee angle showed close agreement for all subjects. Although the models contained simplifications regarding material properties and geometry, the difference between computational and experimental results for all subjects indicate that the finite element models developed in this work accurately 89 90 represent the thigh compression responses for different size people using the same material properties for soft tissue. The objectives completed by this thesis work are important steps toward tools for seat design that will comfortably accommodate people. This project provides a first step in using a computational tool in seat cushion design. This is an effective tool which could be used for the study of seat cushion material properties and different cushion geometries. Work is ongoing to measure and model the responses of soft tissue compression interacting with cushion materials. The recommendations for future work and to improve the finite element model itselfare to: 1. Model and measure more realistic geometries of the internal biological tissues of the human thighs in three-dimensional space. 2. Use different material properties for the anatomical components in the thighs. such as muscle, fat, and skin. . 3. Model and measure the interaction between human thighs and cushion materials. Refinements of the model may lead to better measuring and modeling thigh compression responses on supporting cushion surface. REFERENCES REFERENCES 1. Hubbard, R.P., Hass, W.A., Boughner, R.L., Canole, RA, and Bush, N.J., ”New Biomechanical Models for Automotive Seat Design",§ee__ei_An1e,_ Eng, Paper 930110, 1993. 2. Haas, W.A., "Geometric Model and Spinal Motions of the Average Male in Seated Postures", Masters Thesis, Michigan State University, 1989. 3. Cao, C., Hubbard, RP, and Soutas-Little, R.W., "A Kinematic Study of Human Thorax Flexion and Extension Relative to Pelvis for Computer Simulation of Sitting", Submitted to Journal of Biomechanics. 4. Boughner, R.L., ”A Model of Average Adult Male Human Skeletal and Leg Muscle Geometry and Hamstring Length for Automotive Seat Designers”, Masters Thesis, Michigan State University, 1991. 5. Hubbard, R.P., and D.G. Mcleod, "A Basis for Crash Dummy Skull and Head Geometry”, WW. Plenum Press. N.Y.. 1973. 6. Hubbard, R. P. and D. G. Mcleod, "Definition and Development of a Crash Test Dummy Head”. WW. paper no 741193, pp. 599- 628, Soc. Auto. Engin., 1974. 7. Robbins, D.H., "Anthropometric Specifications for Mid-sized Male Dummy", Vol. 2, Fin. Rep. No. DOT-HS-806-716, US. Dept. of Trans, NHTSA, 1985. 8. Reynolds, H. M., C.C. Snow, andJ.W. Young, 'Spatral Geometry of the Human Pelvis", FAA-AM-82- 9, CivilAeromedical Inst, Fed. Aviation Admin., 1982. 9. Bush, N.J., "Two-Dimensional Drafting Template and Three-Dimensional Computer Model Representing the Average Adult Male in Automotive Seated Postures", Masters Thesis, Michigan State University, 1992. 10. Chow, W. W. and Odell, E. I., ”Deformation and Stresses In Soft Body Tlssues of a Sitting Person"ASME_.loumaLef.Biomed1anicaL Engineering, 100: 79-87, 1978. 11. Reddy, N. P. Brunski, J. B. Patel, H., and Cochran, G. V. 8., ”Stress Distributions In a Loaded Buttock with Various Seat Cushions” ,Adveneee MW PP 97-100 1980- 91 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 92 Brunski, J. B., Roth, V., Reddy, N. P, and Cochran, G. V. 8., "Finite Element Stress Analysis of a Contact Problem Pertaining to Formation of Pressure Sores“ Wm 99 53-56 1980 Yamada, H., StrengtneLBigiegjeaLMaterjeie, (F.G. Evans, ed.), WIlliams and Wilkins 00., Baltimore. PP 231, 1970. Sacks, A.H., O'Neill, H., and Perkash, l., "Skin Blood Flow Changes and Tissue Deformations Caused by Cylindrical Indentors", JeumeLgLBeneb. BED, 22: 1-6, 1985. Krouskop, T.A., Dougherty, DR, and Vinson, F.S., "A Pulsed Doppler Ultrasonic System for Making Non-invasive Measurements of the Mechanical Properties of Soft Tissues” HJenmeLeLBehem 24: 1-8, 1987. Steege, J. W., Schnur, D. S., and Childress, D. 8., "Prediction of Pressure at the Below-Knee Socket Interface by Finite Element Analysis, ASME W 99 39-43 1 987. Steege, J. W. and Childress, D. S, ”Finite Element Modeling of the Below- Knee Socket and Limb: Phase II”, AWN. WWI: 99121-129 1988 Vannah, W. M. and Childress, D. S., "An Investigation of the Three- Dimensional Mechanical Response of Bulk Muscular Trssue: Experimental Methods and Results”,AS_ME_$ymngeium_en_Qerneu1etienel anadmfliomecbaniszs pp 493-503 1988 Seglind, L.J., Aepiied_Eini1e_E|emeni_Anelyeie, John Wiley 00., 1984. Hollinshead, W.H. and Rosse,C.,Iex1bee|s_ef_Anaierny, Happer & Row, Publishers, Inc., Philadelphia, pp 376-390, 1985. ABAQUS 5.3 Finite Element Package, Hibbitt, Karlsson, and Sorensen Inc. 1993. Hughes IMF. and Gaylord E.W.. WW. McGraw-Hill, New York, pp 59, 1964. ' Zienkiewioz, 00. WW. McGraw-Hill, New York, 1971 . SDRC IDEAS 4.0 Solid Modeling Package and Finite Element Package, Structural Dynamics Research Corporation, Milford, Ohio, 1991. 93 25. SENSOTEC Catalog, Columbus, Ohio, 1993. 26. Haut, R.C., "A Method for Characterizing the Impact Response of the SUPGrficial Musculature". W. 1976. APPENDICES APPENDIX A ABAQUS data files were written for each subject to describe the geometry, the element type, the interface elements, the material properties, and the boundary conditions of the model using standard ABAQUS commands. Same material properties were used for all the subjects with model geometries that were specific to each subject. A typical data file for one subject was shown on the following page. 94 95' T'HEADING.UNSYMM THE STUDY OF COMPRESSION RESPONSES OF HUMAN THIGHS INTERACTING WITH A RIGID FLAT PLATE lN 2-D SPACE. Units: N, mm *NODE 2561, 0.,55. 33, 55.0. 1281, 0.,0. 1. 0.,-55. *NODE,NSET=N3000 3000, 35..-55. *NODE,NSET=N3001 3001, 0.77. *NGEN,NSET=NY 1,1281.40 *NGEN.NSET=NY 1281 .2561 .40 *NGEN.LINE=C 1,33 *NGEN,LINE=C 332561.79 *NGEN 33,1281,39 *NGEN 3,1203,40 5,1125,40 7.1047.40 9,969.40 11,891.40 13,813.40 15,735.40 17,657.40 19,579.40 21,501.40 23,423.40 25,345.40 27,267.40 29,189.40 31,111.40 1203,2403.40 1 125,2245,40 1047,2087,40 969.1929.40 891,1771,40 813,1613,40 735.1455,40 657.1 297.40 579.1 139.40 501 .981 .40 423,823.40 345,665.40 267,507.40 1 89,349.40 1 1 1 .191 .40 *NGEN 1 201 .1 203 1 121 .1 123 1 123.1 125 1 041 ,1 043 1 043.1 045 1045.1 047 961 .963 963.965 965.967 967.969 881 .883 883.885 885.887 887.889 889.891 801 .803 803.805 805.807 807,809 809.81 1 81 1 .813 721 .723 723,725 725,727 727.729 729.731 731 .733 733.735 641 .643 643,645 645.647 647,649 649,651 651 .653 653.655 655.657 561 .563 563.565 565.567 567.569 569.571 571 .573 573,575 575,577 577,579 431 .433 433,435 485,487 437.439 489.491 491 .493 493.495 495,497 497,499 499,501 401 .403 403,405 405,407 407,409 409.41 1 41 1 .413 413,41 5 415,417 417,419 419,421 421 .423 321 .323 323,325 325,327 327,329 329,331 331 .333 333,335 335.337 337.339 339.341 341 .343 343.345 241 .243 243,245 245,247 247,249 249,251 97 251.253 253.255 255,257 257,259 259.261 261.263 263.265 265.267 161,163 163.165 165.167 167.169 169,171 171.173 173.175 175.177 177.179 179.181 181.183 183.185 185.187 187,189 81.83 83.85 85.87 87.89 89.91 91.93 93.95 95.97 97.99 99.101 101,103 103.105 105.107 107.109 109.1 11 1203.1361.79 . 1 125.1283.79 1283,1441 .79 1047.1205,79 1205.1363.79 1363,1521 .79 969.1 127.79 1127,1285,79 1285.1443,79 98 1443,1601 .79 891 .1049.79 1 049,1207.79 1207,1365.79 1 365.1 523.79 , 1523,1681 .79 813.971 .79 971 ,1 129.79 1129.1287.79 1287.1445,79 1445.1603,79 1603,1761 .79 735,893.79 893.1051 .79 1051,1209.79 1209.1367,79 1367.1525,79 1 525,1683,79 1683,1841 .79 657,815.79 815,973.79 973.1 131 .79 1131.1289,79 1289.1447.79 1447,1605.79 1605.1763.79 1763,1921 .79 579,737.79 737,895.79 895.1053.79 1053,1211.79 1211 .1369.79 1369.1527.79 1 527.1685.79 1685.1843.79 1843,2001 .79 501 .659.79 659,817.79 81 7,975.79 975.1 133.79 1133.1291.79 1291.1449,79 1449,1607.79 1 607.1765,79 ' 1 765.1 923.79 1 923.2081 .79 99 423.581 .79 581 .739.79 739,897.79 897.1 055.79 1055.1213.79 1213,1371 .79 1371.1529.79 1529.1 687,79 1687.1 845.79 1 845.2003.79 2003,2161 .79 ' 345,503.79 503,661 .79 661 .81 9,79 81 9,977.79 977.1 135.79 1 135.1293.79 1293.1451 .79 1451.1609.79 1 609.1 767.79 1767.1 925.79 1 925.2083.79 2083,2241 .79 267,425.79 425,583.79 583,741 .79 741 .899.79 899.1 057.79 1057,1215.79 1215.1373,79 1373,1531 .79 1531.1689.79 1 689.1 847.79 1 847.2005.79 2005.21 63.79 2163,2321 .79 1 89,347.79 347.505.79 505,663.79 663.821 .79 821 .979,79 979.1 137.79 1137,1295,79 1 295.1 453 .79 1453,1611 .79 1611 ,1769,79 100 101 1769,1927.79 1927203579 2035224579 2243,2401 .79 1 1 1,269.79 269,427.79 427,535.79 535,743.79 743.901 .79 901 .1059.79 1059.1217,79 1217.137579 1375153579 1533,1691 .79 1691 .1349.79 1349,2007,79 , 2007216579 2165,2323,79 2323,2431 .79 *ELEMENT.TYPE=CPE8RH,ELSET=MUSCLE 1,1.3,33.31.2.43.32.41 16.3,53533,4.4534,43 30.5.7,87.85,6,47,86,45 43,7,9,39,37,3.49,33,47 55.9.11.91,39.10.51,90,49 66.11.13,93,91.12,53.92.51 7513.1595.93.14.5594,53 85,15,17.97.95.16.57.96.55 93,17,19.99.97,13,59,93,57 100.19.21.101.9920,61.100.59 106,21,23.103.10122.63.102.61 11123.25105.103.24.65.104,63 115.25,27.107,105,26.67.106.65 1 18.27,29.109,107.28.69.108,67 12029.31,111.109.30.71.110.69 153,1203.1283.1441.1361.1243,1362,1401.1282 168,1125,1205,1363.1283.1165,1284.1323.1204 132.1047,1127.123512051037,1206,1245.1126 195.969.1049.1207,1127.1009,1128.1167.1048 207.391,971.11251049231 ,1050.1039.970 213,313.393,1051.971253,972,1011,392 223,735.315,973,393,775394.933,314 237,657.737,895.815.697,816.855.736 245.579.659.317,737,619.733,777,653 252,501 .531 .739.659.541 ,660.699.530 253.423.503.661 .531 ,463,532,621,502 102 263.345.425.583.503,385.504.543.424 267.267.347.505,425,307.426,465.346 270.1 89 .269.427.347,229.348.387,268 272.111.191.349.269,151.270.309.190 *ELEMENT,TYPE=CPE6H.ELSET=MUSCLE 121.31.33.111.32.72.71 137.33.191.111.112.151.72 'ELGEN.ELSET=MUSCLE 1 .15.80.1 16.14.80,1 30.13,80.1 43.12,80,1 55,1 1.80.1 66,10.80,1 76,9.80.1 85.8.80,1 93.7.80.1 100.6,80,1 106.5.80.1 1 11,4.80.1 1 15.3.80.1 1 18.2,80,1 153.15.80.1 168.14.80.1 182.13.80,1 195.12.80.1 207.1 1 .80.1 218.10.80,1 228.9.80.1 237.8.80.1 245.7.80.1 252.6,80.1 258,5,80.1 263.4.80.1 267.3.80,1 270.2.80,1 121 .16.78.1 137.16,78,1 *ELEMENT.TYPE=IR822.ELSET=BOTSU RF 401.1 .2.3.3000 'ELGEN.ELSET=BOTSU RF 401 .15,2.1 ‘ELEMENT.TYPE=IR822.ELSET=TOPSU RF 501.191,270.349.3001 'ELGEN.ELSET=TOPSURF 501 ,15,158,1 103 *RIGID SURFACE,TYPE=SEGMENTS.ELSET=TOPSURF START,0.1 274.98.9996 CIRCL.O..55.,0..77. *RIGID SURFACE,TYPE=SEGMENTS.ELSET=BOTSURF START.0.,-55. LINE.70.,-55. *SOLID SECTION,ELSET=MUSCLE,MATERIAL=A1 *MATERIAL.NAME=A1 *HYPERELASTIC.N=1 1.43E-3, 0.0. 14.08 *INTERFACE.ELSET=BOTSU RF *SURFACE CONTACT.NO SEPARATION *FRICTION.ROUGH *INTERFACE.ELSET=TOPSU RF *SURFACE CONTACT.NO SEPARATION *FRICTION,ROUGH *ELSET.ELSET=BOT 1 .16.30.43.55.66.76.85.93.100. 106,111,115.118,120 *NSET,NSET=SIDE 33 *BOUNDARY NY,XSYMM N3000,1 N3000.6 N3001.1 N3001,2 . N3001 .6 *RESTART.WRITE.FREQ=1 0 *STEP.NLGEOM.INC=100 *STATIC 0.05.1 .0.1E-6.0.1 *BOUNDARY N3000,2,2.80. ’NODE PRINT.FREQ=1.NSET=N3000.SUMMARY=NO U2.RF2 *NODE PRINT.FREQ=1 ,NSET=N3001,SUMMARY=NO U2.RF2 *NODE PRINT.FREQ=1.NSET=SIDE.SUMMARY=NO U1 ,U2 *EL 8 *EL PRINT,FREQ=50.ELSET=BOT.TOTALS=YES S *EL FILE,ELSET=MUSCLE.FREQ=10.POSITION=NODES PRINT.FREQ=50.ELSET=MUSCLE.POSITION=CENTROIDAL,TOTALS=YES 104 S E ENER *NODE FILE.NSET=N3000.FREQ=2 U.RF,CF *NODE FILE.NSET=N3001.FREQ=2 U.RF,CF *NODE FILE.NSET=SIDE.FREQ=2 U *END STEP APPENDIX B CONSENT FORM FOR THE NON-INVASIVE MEASUREMENT OF DEFORMATIONS AND LOADS IN THE HUMAN THIGHS OF SEATED POSTU RES Human subjects participating in the experiments signed the consent form, shown on the following page. 105 106 INFORMED CONSENT STATEMENT l. . consent to serve as an experimental subject in the research project. “Non-invasive measurement of deformations and loads in the thighs and buttocks of sitting people.” I have thoroughly informed of the purpose and procedures in which I will participate. I have been advised that all work will be conducted under the supervision on individuals who are expert with loads and deformations measurement. I understand that the test is non-invasive. I have been assured that my participation remains confidential, and published experimental results will not reveal my identity. My consent to serve as a subject is given freely and without coercion. Further. I understand that I may withdraw from this experiment at any time and for any reason of my choice. SUBJECTS SIGNATURE DATA TYPED OR PRINTED NAME ADDRESS PHONE NUMBER WITNESS DATA APPENDIX C PROTOCOL FOR NON-INVASIVE MEASUREMENT OF DEFORMATIONS AND A. LOADS IN THE HUMAN THIGHS OF SEATED POSTURES Parameter measurement techniques . Find the position of right and left Anterior Superior Iliac Spine (ASIS). Mark the two points, with a washable pen. and measure the distance between them. This is the defined Hip Width. Find the position of right femur Greater Trochanter and Lateral Condyle of Femur. Mark the two points and measure the distance between them. This is the Hip-to-Knee Length. Find the position of right Lateral Malleolus. Mark this point. Measure the distance between the Lateral Condyle of Femur and Lateral Malleolus. This is the Knee-to-Foot Length. Also, without shoes. measure the distance from bottom of foot to knee pivot. This is Leg Length. Subject lies prone (stomach down) on a flat. horizontal surface so that the right and left ASIS and the pubic symphsis is in contact with the flat surface. Place a 5" by 12" flat board across the "flat" part of the upper rear of the pelvis, across the sacral region at the level of the right and left Posterior Superior Iliac Spine (PSIS). and measure the angle of this board relative to the horizontal surface with an angle finder. This is the angle between anatomical definition of Hip Angle and measurements of Hip Angie. 107 108 . Measure the weight and the height of the subject. Force and deformation measurement techniques . Before subject is in chair, adjust the knee pivot according to the Hip-to-Knee length. . Adjust the foot rest plate according to the Leg Length. So knee pivot aligns with Lateral Condyle of Femur. . Position the jack and the testing surface in the thigh length direction. The surface is under 1/2 of thigh length from Greater Trochanter. . Subject sits on the chair with shorts in a normal posture (with the knee angle equal to 90 degrees and the torso straight up). . Check the placement of the ischial tuberosities. . Position the lumbar support plate against the flat part of the upper rear of the pelvis as in AA. . Adjust the testing surface of the thigh in the lateral direction, the thigh is in the middle of the testing surface. . Position the back support. TIghten all adjustment of the chair. 109 9. Subject sits on the chair in a normal posture. Relax for 1 minute. 10. Locate and mark the test portion on the thigh. Measure the Thigh Side-to- Side Width and Thigh Front-to-Rear Thickness with a caliper. Measure the circumference and the distance from the bottom of thigh to a straight line between the Great Trochanter of the hip and the lateral Condyle of the knee. 11. Put the belt on the top of the knee joint of the testing thigh (lower leg support is vertical). There is only a little tension in the belt. Subject with arms straight down. not resting on legs. 12. Slowly raise the test surface to the back of the thigh up to just before contact. Begin to run the test program. Record the movement of the jack. Set the readings of the electronic depth gauges to zero. Don't reset for later tests with same subject. Be sure the units are mm. Give a file name to keep the collecting data. The file name is .csv file with subject initials in the first three spaces, knee angle the next three spaces and trial number in the last two spaces. such as, RPHk9001.csv. 13. Pump the jack one full stroke and wait for 10 seconds. then push the space bar to collect data. The test should be terminated when the subject's foot is raised by the jack. 14. Collect data for three trials under same condition. Then. change the knee angle and repeat the above procedures for knee angles of 120. 150. and 165 degrees. APPENDIX D THE STANDARD ERROR CALCULATION BETWEEN EXPERIMENTAL AND COMPUTATIONAL RESULTS The standard error calculation Was based on treating the testing data as real value. The differences between experimental and computational results are calculated for every 5 mm increment of vertical displacement. If we assume that at certain vertical displacement point, the testing value is T. the model result is M, then the standard error. 5., in absolute value is: n 2 2(M-T) Sr: 51—":— (0.1) where n is the total number of data points. The standard error 5. in percentage is: s.= ——-— x 100% (0-2) 110