## 3 Results and Discussion
### Mechanical Characterization of Cellular Structures and Insoles
#### 3.1.2 Deformation and Stress Analysis via FEM of Insoles
In the insole with TPMS cellular structure with 10.33% relative density, the stress was concentrated on the walls of the unit cells because the walls were thin, approximately 0.2 mm (see Figure 12d). Figure 11: Static simulation displacement results in cellular structures in the insole: (**a**) insole with BCC cellular structure, 10.33%; (**b**) insole with BCC cellular structure, 14.67%; (**c**) insole with BCC cellular structure, 20.19%; (**d**) insole with TMPS cellular structure, 10.33%; (**e**) insole with TPMS cellular structure, 14.67%; (**f**) insole with TPMS cellular structure, 20.19%; and (**g**) solid insole. For the insoles shown in Figure 12e,f, the stress was concentrated in the union of the top surface of the insole with the unit cell. The walls in these insoles were thicker. Figure 12g shows that the stress was concentrated on the periphery of the insole near the lateral rear foot area. In the insoles with BCC cellular structure, the Von Mises stress increased as the relative density decreased. This effect occurred because the cellular structure with lower relative density had thinner struts in its unit cell. This resulted in a higher stress concentration between the top of the surface and the strut (see Figure 12a-c). The insoles that used TPMS cellular structure did not exhibit this tendency; the cellular structure with lower relative density had a stress concentration in the walls of the unit cells because they were thin (see Figure 12d). The other insoles with TPMS cellular structure concentrated the stress between the surface of the insole and the unit cell (see Figure 12e,f). In light of a potential exposure to variable loading conditions, such as the those encountered when the person is walking or jogging, insoles must provide impact absorption. It has been shown that bending-dominated structures offer a more cushioning response that could benefit these conditions [34]. Hence, the topology that presents the bending-dominated deformation mechanism is the best option to be implemented in the insole, since it is the one that absorbs the highest energy. Figure 12: Static simulation Von Mises stress results in an insole with cellular structures into the insole: (**a**) inside with BCC cellular structure, 10.33%; (**b**) inside with BCC cellular structure, 14.67%; (**c**) inside with BCC cellular structure, 20.19%; (**d**) inside with TMPS cellular structure, 10.33%; (**e**) inside with TPMS cellular structure, 14.67%; (**f**) inside with TPMS cellular structure, 20.19%; and (**g**) solid insole. According to Table 4, the insoles with the lowest displacement and Von Mises stress were the solid insole and the insole with the BCC cellular structure with 20.19% relative density. The results of these models were compared with the insoles designed by [PERSON] et al. (2015), [PERSON] (2016), and [PERSON] et al. (2017) in Table 5.  
The solid insoles had stress concentrations lower than 1 MPa, the same as the models reported in ([PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 2015) (see Table 5). The stress was concentrated on the periphery of the insole, near the area where the fixed support was placed. Furthermore, the stresses in the solid insole were evenly distributed over its entire surface (see Figure 12g). On the other hand, in the model with cellular structure, it is observed that the stress distribution was uneven; stress concentration was observed in regions of the cellular materials. The stress is concentrated at the joint of the struts of the unit cell with the surface of the insole and is transferred to the external part of the insole. Identifying stress concentrations in porous materials allows the designer to iterate between various topologies, while keeping the same volume fraction but targeting the region of the stress concentration. The stress presented in these insoles does not exceed the elastic limit of the material. Therefore, under the conditions simulated, the implementation of cellular structures is feasible.