## 3 Materials and Method
### Design Phase
#### 3.1.1 Geometry Optimization: 2D FE Model
The middle blade, which had a straight profile in the sagittal plane, was defined only by its length (MB\({}_{L}\)) and thickness (MB\({}_{t}\)). The lower blade, provided by Ossur, had been already optimized, in terms of shape and material properties, for specific users' weight categories. Figure 4: Schematic image of the boundary conditions used for the 2D FE model of the _Design_ step, which was used to simulate the static tests according to ISO 10328. The heel was loaded with an inclined platform (\(-15^{\circ}\)) to which a displacement was imposed (10 mm); the forefoot was compressed with a \(20^{\circ}\) inclined platform which was moved until 50 mm. In both cases, the platform was free to move along its longitudinal direction. _Mesh modeling._ The FE model was built in ANSYS Workbench. PLANE183 (ANSYS) elements were used for mesh building; these were two-dimensional 8- and 6-node elements with quadratic displacement behavior and two translations at each node as degrees of freedom. The final 2D FE model of MyFlex-\(\gamma\) was meshed (Figure 6), presenting a total of 10,000 nodes corresponding to 20,000 degrees of freedom. _Contacts modeling._ The contacts between parts had to be modeled differently according to the real conditions. For parts that worked bending toward each other with slight sliding, the contacts were modeled as _frictional_ using _pure penalty formulation_ and 0.1 was set as  
Figure 5: Geometric parameters of MyFlex-\(\gamma\) varied in the 2D FE model of the _design phase_—see Table 3.  
Figure 6: Mesh modeling and width assignment in the transversal direction. The 2D FE model was meshed with PLANE183 elements, for a total of 10,000 nodes without the platform and 20,000 with the platform. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Min Value** & **Max Value** & \\ \hline upper blade thickness UB\({}_{\text{I}}\) (mm) & 6.00 & 8.50 & defined in step 2 \\ upper blade curvature 1 UB \({}_{\text{c1}}\) (deg) & 1.00 & 3.00 & \\ upper blade curvature 2 UB \({}_{\text{c2}}\) (deg) & 1.00 & 3.00 & \\ upper blade curvature 3 UB \({}_{\text{c3}}\) (deg) & 1.00 & 3.00 & \\ upper blade curvature 4 UB \({}_{\text{c4}}\) (deg) & 1.00 & 3.00 & \\ upper blade curvature 5 UB \({}_{\text{c5}}\) (deg) & 3.00 & 5.00 & \\ middle blade length MB\({}_{\text{I}}\) (mm) & 150 & 175 & \\ middle blade thickness MB\({}_{\text{I}}\) (mm) & 7.00 & 10.00 & defined in step 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric parameters of MyFlex-\(\gamma\) varied in the 2D FE model of the _design phase_—see Figure 5.  
the _normal stiffness factor_. For contacts that could be modeled as glued/bonded, the _bonded_ contact type was used with _augmented Lagrange formulation_ and \(1\) was set as the _normal stiffness factor_. In the present work, the upper blade, middle blade and lower blade bent toward each other with slight sliding when the foot was loaded. Therefore, the contacts between the upper blade and middle blade and between the middle blade and the lower blade were modeled as _frictional contact_ using _pure penalty formulation_. The ankle frame and the upper blade were joined together with two M8 bolts along the longitudinal direction; for this condition, the contact between the ankle frame bottom surface and the upper blade top surface could be modeled as _bonded_ to simplify the simulation, using _augmented Lagrange formulation_. A summary of the contacts is presented in Table 4.  
For the 2D FE model of MyFlex-\(\gamma\), a _no-separation_ contact type between the tube connector and the ankle frame (see Figure 7) was used to model the ankle joint; a _no-separation_ contact type allows frictionless motions to be performed without separation of the parts. _Joints_: Pretensioned bolts were modeled as preloaded springs, where the preload given as force was equal to the bolt pretension of the corresponding bolt. More specifically, the bolts were modeled as _longitudinal springs body-to-body joints_ (longitudinal COMBIN14, ANSYS).