## 2 Method
### FE Model  
The 2D FE model of the human lower limb was created using Abaqus(r) software (Version 6.12, Dassault Systemes, Velizy-Villacoublay, France) and features the foot (calcaneus, talus, metatarsus lumped together, tarsus lumped together), leg (tibia bone), thigh (femur bone), soft tissues, ankle, knee, hip joints and trunk (Figure 2). The femur and tibia bones were made of a central part of cortical bone and trabecular bones at the ends. The bones were held together by soft tissues, which represent muscles, skin, tendons and adipose tissue. Bones are in contact at joints; however, joint cartilage has not been modeled. The anthropometric dimensions used to create the model have been retrieved from several references (Table 2) and calculated for a virtual subject 175 cm tall. Obviously, the natural modes and frequencies are strongly dependent on these anthropometric dimensions, yet focusing on a single virtual subject showed promising results and allowed us to validate the methodology.  
The model was developed for a standing posture without knee flexion. Humans are indeed exposed to vibrations and impacts while extending legs. In industry, workers are liable to stand on platforms, which are sources of vibrations, and it is common to remain standing in public transport.  
Four materials were used: trabecular and cortical bones and soft tissues for the trunk. All of the components of the trunk (spine, scapular, abdomen, etc.) were lumped together (see Figure 2) to simplify the model, as defined by [PERSON] [12]. Mechanical properties of the bones [24], soft tissues and trunk [12] are summarized in Table 3. The downside regarding the use of a linear elastic constitutive law for soft tissues is discussed in Section 4. Fixed boundary conditions were applied at the shoulder to allow motion of the trunk and hence the pelvis. The mesh is created using default CPS33-node linear plane stress triangle elements, for a total of 1167 nodes and 1742 elements. Modal analyses of the model were then performed using Abaqus(r) on a standard workstation. Modal frequencies' sensitivity to the mesh density was investigated.  
\begin{table}
\begin{tabular}{c l c} \hline \hline
**Segment** & **Parameters** & **Dimension (mm)** \\ \hline \multirow{8}{*}{Thigh} & Femoral length [25] & 482.0 \\  & Femoral head diameter [26] & 46.1 \\  & Neck width of the femoral head [26] & 24.1 \\  & Femoral diaphragysiswidth [27] & 30.0 \\  & Femoral condyles width [28] & 81.4 \\  & Thigh diameter [29] & 191.0 \\  & Knee radius [29] & 125.4 \\ \hline \multirow{4}{*}{Leg} & Tibia length [28] & 383.4 \\  & Tibia width (13.7 cm above ankle) [30] & 28.2 \\  & Tibia proximal epiphysis width [31] & 60.1 \\  & Tibia distal epiphysis width [31] & 43.6 \\  & Calf radius [29] & 119.7 \\ \hline \multirow{3}{*}{Foot} & Foot length [32] & 260.0 \\  & Foot height [33] & 81.2 \\ \cline{1-1}  & Ankle height [33] & 127.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Anthropometric table for a virtual subject 175 cm tall.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Body Zones**} & \multicolumn{3}{c}{**Initial**} & \multicolumn{3}{c}{**Updated**} \\ \cline{2-5}  & \(E\) **(MPa)** & \(D\) \(\left(\mathbf{10^{3}}\text{ kg/m}^{3}\right)\) & \(E\) **(MPa)** & \(D\) \(\left(\mathbf{10^{3}}\text{ kg/m}^{3}\right)\) \\ \hline Trunk & 600 & 1.00 & 600 & 1.30 \\ Cortical & 17,500 & 2.10 & 17,500 & 2.10 \\ Trabecular & 450 & 1.80 & 450 & 1.80 \\ Soft tissues & 345 & 1.20 & 615 & 1.11 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Initial and updated mechanical properties. _E_: Young modulus, _D_: Density.  
Figure 2: Numerical model of lower limb (left); mesh detail of hip joint region (right).