## 3 Results and Discussion
The forces in the incremental forming process are obtained from a file provided by the Ls-Dyna program, called crfcor, which contains the contact forces between the different parts making contact. The summary of the results obtained both experimentally and by simulation for forces is given in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Material** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{**Material Model**} & \multicolumn{2}{c}{**Strain on x**} & \multirow{2}{*}{**Strain on y**} & \multirow{2}{*}{**Major Strain \(\varepsilon_{1}\)**} & \multirow{2}{*}{**Minor Strain \(\varepsilon_{2}\)**} & **Thickness** \\  & & & **Direction \(\varepsilon_{\chi}\)** & & **Direction \(\varepsilon_{\chi}\)** & **[\%]** & **[\%]** \\ \hline \multirow{2}{*}{PA} & 24 & 2.55 & 1.44 & 0.52 & 14.70 & 0.52 \\ \cline{2-7}  & 89 & 4.21 & 2.74 & 2.84 & 15.55 & 2.99 \\ \hline \multirow{2}{*}{PE} & 24 & 4.63 & 1.38 & 4.63 & 6.58 & 4.52 \\ \cline{2-7}  & 89 & 4.21 & 1.85 & 1.59 & 9.29 & 3.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific strain and thickness reduction differences between experimental and simulated values for polyamide and polyethylene. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Material** & **F\({}_{\mathbf{z}}\) Force** & **F\({}_{\mathbf{x}}\) Force** & **F\({}_{\mathbf{y}}\) Force** \\
**Type** & **Model** & **[kN]** & **[kN]** & **[kN]** \\ \hline PA & 24 & 0.91 & 0.50 & 0.50 \\ \hline PA & 89 & 0.89 & 0.49 & 0.49 \\ \hline Experimental PA & 0.87 & 0.48 & 0.48 \\ \hline PE & 24 & 0.57 & 0.36 & 0.36 \\ \hline PE & 89 & 0.56 & 0.35 & 0.35 \\ \hline Experimental PE & 0.54 & 0.34 & 0.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results obtained for forces for polyamide and polyethylene. Figure 7: (**a**) Force variation on z direction for FEM using material 89 for simulating PA 6.6; (**b**) force variation on z direction determined experimentally for PA 6.6; (**c**) force variation on x direction for FEM using material 89 for simulating PA 6.6; (**d**) force variation on x direction determined experimentally for PA 6.6; (**e**) force variation on y direction for FEM using material 89 for simulating PA 6.6; (**f**) force variation on y direction determined experimentally for PA 6.6. An analysis of the data presented in Table 3 shows that for forces, the values closest to the ones obtained experimentally are given by material 89. In both the numerical simulation and the performed experiments, the maximum values obtained for the forces in polyamide are higher than those obtained for polyethylene. In contrast to the analysis of strains, in the case of the forces in the process, the values obtained from the simulation are higher than the values obtained experimentally when using both material model 24 and material model 89. The differences given by material model 24 for polyamide are 4.23% for the F\({}_{\mathrm{z}}\) force, 4.74% for the F\({}_{\mathrm{x}}\) force and 4.56% for the F\({}_{\mathrm{y}}\) force, as presented in Table 4. The differences given by material model 89 for polyamide are 1.83% for the F\({}_{\mathrm{z}}\) force, 2.24% for the F\({}_{\mathrm{x}}\) force and 2.54% for the F\({}_{\mathrm{y}}\) force. Figure 8: (**a**) Force variation on \(z\) direction for FEM using material 89 for simulating PEHD 1000; (**b**) force variation on \(z\) direction determined experimentally for PEHD 1000; (**c**) force variation on \(x\) direction for FEM using material 89 for simulating PEHD 1000; (**d**) force variation on \(x\) direction determined experimentally for PEHD 1000; (**e**) force variation on \(y\) direction for FEM using material 89 for simulating PEHD 1000; (**f**) force variation on \(y\) direction determined experimentally for PEHD 1000.