## 3 Materials and Method
### Functionality Verification Phase
#### 3.3.3. ISO 22675-ISO/TS 16955 Dynamic Test  
The re-adapted 2D FE model of the foot prosthesis was used to build the present model to simulate the ISO 22675-ISO/TS 16955 dynamic/roll-over test. Other parts were added, such as the shank, the thigh and the tilting table (Figure 20). The contacts, mesh modeling, joints, materials and width (dimension in the transverse direction) were the same used in the first step of the _design phase_. The connection between the shank and the ankle-foot system was modeled as a bonded contact. The contact between the knee portion of the thigh and the knee portion of the shank was modeled in the FE model as a _no-separation_ contact to create the knee joint. The thigh remained vertical and was free to move along the vertical direction only. The tilting table was rotated according to ISO 22675-ISO/TS 16955, while the _M-shaped force_ was imposed from the top of the thigh (Figure 20). The angle between the foot and the tilting table ranged from \(-20^{\circ}\) to \(40^{\circ}\) (Figure 20). The rotation of the foot during the roll-over test was calculated using the virtual markers G, M, J and K. First of all, the initial coordinates of each marker were determined from the CAD model as G (\(x_{\text{G0}}\);\(y_{\text{G0}}\)), M (\(x_{\text{M0}}\);\(y_{\text{M0}}\)), J (\(x_{\text{J0}}\);\(y_{\text{J0}}\)) and K (\(x_{\text{K0}}\);\(y_{\text{K0}}\)). The displacements of the virtual markers during the roll-over test were direct outputs of the simulation--\(u_{G}\), \(u_{M}\), \(u_{J}\) and \(u_{K}\), in the \(x\)-direction, and \(v_{G}\), \(v_{\text{M}}\), \(v_{J}\) and \(v_{K}\), in the \(y\)-direction. The coordinates of the markers during the roll-over test were: G(\(x_{\text{G0}}+u_{\text{G}}\);\(y_{\text{G0}}+v_{G}\)), M(\(x_{\text{M0}}+u_{\text{M}}\);\(y_{\text{M0}}+v_{M}\)), J(\(x_{\text{J0}}+u_{\text{J}}\);\(y_{\text{J0}}\) + \(v_{J}\)) and K(\(x_{\text{K0}}+u_{\text{K}}\);\(y_{\text{K0}}+v_{K}\)). The rotation \(\Delta\alpha\) of the foot was given as the variation of the angle between the shank axis and the GM line. The angle \(\alpha\) between the shank axis and the GM line was given as follows:  
\[\alpha=\alpha_{s}-\alpha_{GM} \tag{12}\]  
where \(\alpha_{s}\) is the angle between the shank axis and the horizontal direction, calculated as  
\[\alpha_{s}=\arctan\Big{(}\frac{(y_{\text{K0}}+v_{K})-(y_{\text{J0}}+v_{J})}{( x_{\text{K0}}+u_{K})-(x_{\text{J0}}+u_{J})}\Big{)} \tag{13}\]  
whereas \(\alpha_{GM}\) is the angle between the GM line and the horizontal direction, which is calculated as follows:  
\[\alpha_{GM}=\arctan\Big{(}\frac{(y_{\text{G0}}+v_{G})-(y_{\text{M0}}+v_{M})}{ (x_{\text{G0}}+u_{\text{G}})-(x_{\text{M0}}+u_{M})}\Big{)} \tag{14}\]  
The rotation of the foot was then calculated in the following way:  
\[\Delta\alpha=\alpha-\alpha_{0} \tag{15}\]  
with \(\alpha_{0}\) as  
\[\alpha_{0}=\alpha_{s0}-\alpha_{GM0} \tag{16}\]  
Figure 19: M-shaped force: the qualitative behavior of the heel and the forefoot forces are based on ISO 10328 dynamic test, while the maximum values (130% of the body weight for the heel force and 108% for the forefoot force) are from literature—see the _Biomechanical Requirements_ in Section 2.4. In the present work, a 60 kg body weight was used; therefore the peaks were 764 N and 635 N. The forces were imposed as shown in Figure 18.  
where \(\alpha_{50}\) and \(\alpha_{GM0}\) are the initial angle between the shank axis and the horizontal direction and the initial angle between the GM line and the horizontal line, respectively. For the dynamic analysis, an entire gait cycle of 1 s was considered.