## 4 Discussion  
Table 4 represents the numerical simulation results of the 2D rough geometry for the three load cases. It was noticed that von Mises stress was in the range between 0.043 and 0.173 MPa, which were values lower than the yield stress of the VeroWhite material (49.9 MPa). The weight of the structure was equal to 298.2 g. As mentioned before, this study aimed to find a better compromise between weight and strength. By integrating the biomimetic method of L-systems along the PSLs of the structure, it could be possible to reduce the initial weight in a way that the von Mises stress stays lower than the yield stress of the VeroWhite material. To validate the hypothesis, numerical simulations were conducted on six L-systems' structures. The results of von Mises stress and weight were collected in the L9 DOE (Tables 5 and 6). Firstly, by analyzing the von Mises values in Tables 5 and 6, it was noticed that some values were higher than the yield stress of the VeroWhite material. This was the case of the values in experiments 1 to 7 for the CL-1 configuration (Table 5), experiments 1 to 6 for the CSL-1 configuration (Table 5), and experiments 1 to 4 for the SL-2 configuration (Table 6). The following combinations are hereafter excluded and cannot be considered as optimal configurations:  
* For the CL-1 configuration, a thickness of 1.5 mm for the first region and thicknesses of 1, 1.25, and 1.5 mm for the second region cannot be used. Moreover, a thickness of 2 mm for the first region and a thickness of 1.5 mm for the second region cannot be employed together. * For the CSL-1 configuration, thicknesses of 1.5 and 2 mm for the first region cannot be used with any of the thicknesses of the second region (1, 1.25, and 1.5 mm). * For the SL-2 configuration, a thickness of 1.5 mm for the first region cannot be used with any of the thicknesses of the second region. Furthermore, it was noticed that all configurations, including the ones that were excluded from the study, presented a weight value lower than that of the 2D rough structure (298.2 g). The weight reduction percentage is shown in Table 7 below. The weight reduction with respect to the weight of the 2D rough structure was in a range between 74.55 and 86.82%. Logically when the thicknesses of the first and second regions were at level 1 (1.5 and 1 mm, respectively), the weight reduction was the highest. Inversely, when the thicknesses of the first and second regions were at level 3 (2.5 and 1.5 mm, respectively), the weight reduction was the lowest. Figure 16: Study of the effect of the thickness of the first and second regions for the CSL-2 structure. A and B refer, respectively, to the thickness of the first and second regions. (**a**) von Mises stress. (**b**) structure weight. Figure 10 represents the von Mises stress results for each load case and PSLs' direction configuration. It represents particularly the following cases:  
* The case where both regions were at their lowest level 1 (1.5 mm and 1 mm for first and second region, respectively). This case is denoted as Case 1 (a in Figure 10). * The case where both regions had the same thickness (level 1 for the first region and level 3 for the second region). \(\mathrm{f_{FR1}=f_{SR3}=1.5}\) mm. This case is denoted as Case 2 (b in Figure 10). * The case where both regions were at their highest level 3 (2.5 mm and 1.5 mm for the first and second regions, respectively). This case is denoted as Case 3 (c in Figure 10). According to Figure 10, and as expected for the three load cases, the structures that had tree growth along the PSLs and the load direction provided a lower von Mises value than those that had growth orthogonal to the load direction. Until this stage of the study, one could predict that the CL-2 configuration was more suitable for the compressive load case, the SL-1 configuration was more adequate for the shear load case, and the CSL-2 configuration was better than the CSL-1 configuration for the compressive/shear load case.