## 2 Materials and Methods
### Mechanical Properties of Tissues and Ground  
Cortical and trabecular bone mechanical properties are strain rate dependent [36]. Through an approach similar to [PERSON] et al. [36] and by using the Fu-Chang foam material model (LS Dyna, MAT_083) (Appendix B, Table A5), they were modeled as isotropic, heterogenous, and viscoelasticity with different non-linear behaviors in tension and compression (Appendix B). According to [PERSON] et al. [49], the strain rate exerted on the body which can lead to bone failure during a traumatic event can be as big as 25 s\({}^{-1}\). In this study, a wider range of strain rates (0.008-30 s\({}^{-1}\)) [36] was used to ensure coverage of all possible strain rates during falling. The cortical bone was assumed to be homogenous (\(\rho=1.8\) g/cm\({}^{3}\)) and trabecular bone density varied between 0.01 and 1.79 g/cm\({}^{3}\) (corresponding densities starting from marrow cavity to the density at the vicinity of the cortical bone). Densities were implemented to the mesh using the material mapping strategy available in Mimics(r) [45] in which bone grayscale values (i.e., Hounsfield units) in CT images were converted to the densities. The soft tissue covering the greater trochanter, hemipelvis, and thigh is mostly made of muscle. Therefore, it was modeled as a single part in this study, and the hyperelastic model (LS Dyna, MAT_MOONEY-RIVLIN_RUBBER) and parameters proposed by [PERSON] et al. [45] were selected for the parametric studies of V\({}_{\text{Impact}}\) and flooring material effects on acetabular fracture (Appendix B, Table A5). [PERSON] and [PERSON] [50] considered TST as a viscoelastic material and studied the effect of aging on TST stiffness. In the current study, to examine the effect of TST quality (stiffness) changes due to aging on the acetabular fracture, a viscoelastic model (LS Dyna, MAT_061) was established. Muscle and adipose layers of TST have very distinct mechanical properties (bulk, short- and long-term shear modulus) [51]. Using an approach similar to [PERSON] et al. [13] for validating their proposed ballistic gel as a TST surrogate, the viscoelastic soft-tissue model was tailored based on values by [PERSON] et al. [51] and studied through a single element test [52] so that its compressive response would fall within the muscle and adipose tissue stress-strain response (Appendix B, Figure A7). The internal reaction force history within the joints resulted from the models proposed by [PERSON] et al. [45] and [PERSON] et al. [13] as the soft tissues are presented in Appendix B, Figure A8. The parameters obtained were assumed as the baseline (young subject) and were increased by 26% through four equidistances (4 \(\times\) 6.5%), representing progressive stiffening of the TST by aging [50] for the parametric study (Appendix B, Table A5). The articular and sacroiliac cartialges were assumed to be hyperelastic (LS Dyna, MAT_MOONEY-RIVLIN_RUBBER) [13], [45] (Appendix B, Table A5). The impact force is absorbed, dissipated, and transmitted between hemi-pelvises through the fibrous cartilage existing in the public symphysis [53]. Therefore the interpubic disc was modeled as a viscoh hyperelastic material (LS Dyna, MAT_HYPERELASTIC_RUBBER) [38] (Appendix B, Table A5). Seven conventional flooring materials as well as rigid ground were considered to study the effect of flooring material on acetabular fracture: Ceramic tile (LS Dyna, MAT_JOHNSON_HOLMQUIST_CERAMICS) [54], ethylene-vinyl acetate (EVA) foam protective mat (LS Dyna,MAT_OGDEN_RUBBER) [55], linoleum (LS Dyna, MAT_ELASTIC) [56], plywood (LS Dyna, MAT_WOOD_PINE) [57], agglomerated cork (LS Dyna, MAT_LOW_DENSITY_FOAM) [58], concrete (LS Dyna, MAT_CSCM_CONCRET) [59], and multi-layer asphalt pavement (LS Dyna, MAT_PIECEWISE_LINEAR_PLASTICITY) [60]. Rigid ground was used in V\({}_{\text{Impact}}\) and TST quality simulations.