## 3 Materials and Method
### Design Phase
#### 3.1.1 Geometry Optimization: 2D FE Model
The **G** and **M** markers taken into account in (**A**) are referred to the reflective markers (grey circles in (**B**)) considered by [PERSON] et al. [25]. In Equation (10), \(\alpha\) is determined as  
Figure 7.4  
Material Properties Optimization: 3D FE Model  
With the 2D FE model, the profile of the elastic elements and the general geometry of the foot prosthesis in the sagittal plane were defined. The 3D CAD model for the 3D FE model was built upon the geometry obtained in the previous step of the _design phase_ methodology (Section 3.1.1). The elastic elements of ESR feet, in general, are laminate composite and they are built by stacking, in sequence, layers of CFRP (carbon fiber-reinforced plastic) or GFRP (glass fiber-reinforced plastic) prepregs, which are sheets of prepregnated fibers (generally pre-impregnated with resin) and they can be unidirectional or woven. The stiffness of each of the elastic elements of the ESR feet is defined by lamination sequence, type, number, orientation and order of each layer. For MyFlex-\(\gamma\), unidirectional and woven CFRP prepregs were used. The lamination sequence of CFRP prepregs layers was optimized to reach the targeted stiffness, thus meeting the biomechanical requirements defined in Section 2.4. The elastic properties of the CFRP prepregs used are gathered in Figure 7.5  
_Loads and constraints_: The 3D FE model is intended to be validated with a mechanical test on a physical prototype of a foot prosthesis. In the ISO 10328 standard, the foot is loaded with an inclined platform, which means two inclined actuators are required, one for the heel and one for the toe, to compress the foot prosthesis. A dedicated test setup was designed and built (Figure 10) to avoid the necessity of two inclined actuators. The ISO 10328-equivalent test setup was characterized by a vertical piston that pushed a platform upward. The relative inclination between the foot and the platform was created by two different adapters that inclined the foot backwards by 15\({}^{\circ}\) and forwards by 20\({}^{\circ}\). The platform, free to move along the longitudinal direction of the foot, compressed the foot prosthesis, fixed at the top. A vertical displacement was imposed to the platform to compress the foot at the heel and at the toe in two different tests to simulate the _ground \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Type** & **Gramm.** & **Thick.** & \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \(G_{12}\) & \(G_{23}\) & \(G_{13}\) & \(\epsilon_{12}\) & \(\epsilon_{23}\) & \(\epsilon_{13}\) \\ \hline  & **g/m\({}^{2}\)** & **mm** & **GPa** & **GPa** & **GPa** & **GPa** & **GPa** & **GPa** & **-** & **-** & **-** \\ \hline UD & 150 & 0.151 & 112.5 & 7.4 & 7.4 & 4.3 & 2.6 & 4.3 & 0.33 & 0.44 & 0.33 \\ UD & 250 & 0.251 & 112.5 & 7.4 & 7.4 & 4.3 & 2.6 & 4.3 & 0.33 & 0.44 & 0.33 \\ W & 200 & 0.234 & 61.3 & 61.3 & 6.9 & 3.3 & 3.3 & 2.7 & 0.04 & 0.30 & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Orthotropic elasticity of CFRP prepregs used to manufacture the upper blade, middle blade and lower blade. Figure 9: Virtual markers displacement during static dorsiflexion test. Platform displacement at 0 (black and white image) mm vs. platform displacement at 50 mm. reaction forces_ at both the early and the late stance, respectively. The total displacement was 10 mm and 50 mm at the heel and the toe load conditions, respectively, because of the different range of motion of the foot during plantar flexion and dorsiflexion. For the toe load, the platform was moved upward linearly at a rate from 3 mm/s to 4 mm/s. The platform moved linearly along the vertical direction for the heel load to compress the foot at a rate from 0.6 mm/s to 0.8 mm/s. These rate values, both for the plantarflexion and dorsiflexion tests, were chosen for a reason of convergence of the simulations. It was verified that the results did not change if the dorsiflexion simulation was performed at a rate of 3 mm/s or at a rate of 4 mm/s. The exact same applies to the plantarflexion simulation.