## 3 Results and Discussion  
Given the fact that four analyses were performed, two for each type of material, with the two material definition options presented above, the results obtained experimentally were compared with those obtained by the simulation using the finite element method. Figures 5 and 6 show the results obtained for the strains and thickness reduction when using material model 24 for polyamide and material model 89 for polyethylene. For the two figures, the left columns (Figures 5a,c,e,g,i and 6a,c,e,g,i) represent the results of the FEM simulation, while the right columns (Figures 5b,d,f,h,j and 6b,d,f,h,j) represent the experimental results. A summary of the strain results obtained both experimentally and by simulation is given in Table 1.  
All strains are engineering strains, requiring multiplication by 100 for those in the simulation so that they can be compared with the ones obtained experimentally. The figures present the results obtained for the material models for which the results were closer to those obtained experimentally. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \begin{tabular}{c} **Material** \\ **Type** \\ \end{tabular}  & \begin{tabular}{c} **Material** \\ **Model** \\ \end{tabular}  & \begin{tabular}{c} **Strain on x Direction \(\varepsilon_{\mathbf{x}}\)** \\ **[\%]** \\ \end{tabular}  & \begin{tabular}{c} **Major Strain** \\ \(\varepsilon_{\mathbf{y}}\)** \\ \end{tabular}  & \ \begin{tabular}{c} **Minor Strain** \\ \(\varepsilon_{\mathbf{1}}\) \\ **[\%]** \\ \end{tabular}  & \begin{tabular}{c} **Thickness** \\ **Reduction** \\ **[\%]** \\ \end{tabular}  \\ \hline PA & 24 & 129.80 & 129.60 & 132.90 & 9.44 & 58.89 \\ \hline PA & 89 & 127.30 & 127.90 & 129.80 & 9.51 & 57.43 \\ \hline Experimental PA & 133.20 & 131.50 & 133.60 & 8.23 & 59.20 \\ \hline PE & 24 & 92.70 & 92.56 & 94.32 & 10.21 & 50.28 \\ \hline PEFigure 5: _Cont_. Figure 5: **(a) Strain on x direction for FEM using material 24 for simulating PA 6.6; (b) strain on x direction determined experimentally for PA 6.6; (c) strain on y direction for FEM using material 24 for simulating PA 6.6; (d) strain on y direction determined experimentally for PA 6.6; (e) major strain for FEM using material 24 for simulating PA 6.6; (f) major strain determined experimentally for PA 6.6; (g) minor strain for FEM using material 24 for simulating PA 6.6; (h) minor strain determined experimentally for PA 6.6; (i) thickness reduction for FEM using material 24 for simulating PA 6.6; (j) thickness reduction determined experimentally for PA 6.6. **  
Figure 6: _Cont._  
An analysis of Figures 5 and 6 shows that, in most cases, the distribution of specific strains and thickness reduction obtained by numerical simulation is very similar to that obtained experimentally. It can be observed that in both numerical and experimental cases, the specific strains \(\varepsilon_{\rm x}\) and \(\varepsilon_{\rm y}\) reach their maximum values on the wall of the frustum of the cone, in the directions of the axes corresponding to their names. The major strain, \(\varepsilon_{1}\), is relatively uniformly distributed on the wall of the frustum of the cone in both polyamide and polyethylene. The minor strain, \(\varepsilon_{2}\), also reaches its maximum values on the wall of the frustum of the cone, towards its lower base. The thickness reduction has a variation similar to that of the major strain \(\varepsilon_{1}\) for both types of materials. A comparative analysis of the results in Table 1 shows that, with the exception of the minor strain \(\varepsilon_{2}\), which has small values compared to the major strain, for all other types of strains and thickness reduction, material 24 gives results closer to the experimental values than material 89 for polyamide, while model 89 gives better results than model 24 for polyethylene. In many cases of sheet forming processes (such as deep drawing process), it is well known that \(\varepsilon_{1}>\varepsilon_{2}\), but the strain state in single-point incremental forming is different.