## 6 Conclusions  
The primary aim of this work was to demonstrate the necessity of accounting for the phenomenon of work hardening in simulating components derived from cold stamping processes of sheet-metal. Work hardening introduces localized material properties that depend directly on the degree of deformation that occurs during manufacturing. To address this, a stamping simulation was performed to extract deformation data, which were then mapped onto the body using a semi-automatic method. The comparison of the two linear models, one with constant thickness and the other with thickness derived from the stamping simulation, revealed minimal differences in the elastic field. Both models showed similar global behavior, with deviations in displacement measurements at Point C being excessively high and failing to accurately represent real behavior. Specifically, the measured displacement at Point C was 0.413 mm, whereas the uniform thickness model simulated a displacement of 0.175 mm (a deviation of 57.60%) and the mapped thickness model simulated a displacement of 0.194 mm (a deviation of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Displacement**} & \multicolumn{3}{c}{**Residual**} \\ \cline{2-7}  & **Measured** [mm]** & **Simulated** [mm]** & **Deviation** [\%]** & **Measured** [mm]** & **Simulated** [mm]** & **Deviation** [\%]** \\ \hline \multicolumn{7}{c}{**Point A**} \\ \hline Uniform & \multirow{2}{*}{12.48} & 11.83 & 5.20 & 0.69 & 2.79 & 304.20 \\ Mapped & & 11.14 & 10.70 & 0.69 & 0.78 & 13.50 \\ \hline \multicolumn{7}{c}{**Point B**} \\ \hline Uniform & \multirow{2}{*}{3.04} & 2.61 & 14.00 & \multirow{2}{*}{0.20} & 0.75 & 275.30 \\ Mapped & & 2.39 & 21.50 & & 0.22 & 9.60 \\ \hline \multicolumn{7}{c}{**Point C**} \\ \hline Uniform & \multirow{2}{*}{0.847} & 0.53 & 37.30 & \multirow{2}{*}{0.029} & 0.19 & 557.20 \\ Mapped & & 0.71 & 15.70 & & 0.09 & 215.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of measured and simulated displacement and residual values at key points. Figure 17: Stresses on the sheet-metal seat in different views from the (**a**) uniform and (**b**) mapped nonlinear material properties. 53.10%). Differences the in iso-strain and iso-stress curves were negligible. Ultimately, thickness mapping alone did not provide a significant improvement in linear simulations for this specific case, as both models converged to reality with comparable precision. In contrast, the nonlinear models demonstrated more substantial differences. The model with uniform geometric and mechanical properties consistently over-predicted the yield, leading to excessive deviations, particularly at Point C, where results were considered unacceptable. The mapped model, while also exceeding the 10% error threshold, showed greater consistency across all sampling points, with errors typically in the range of 10-20%. For example, at Point A, the measured displacement was 5.60 mm, while the uniform model simulated a displacement of 4.88 mm (a deviation of 12.90%) and the mapped model simulated a displacement of 5.11 mm (a deviation of 8.70%). Residual measurements further emphasized the limitations of the standard model, which exhibited excessive yielding and poor agreement with experimental results. The mapped model, however, provided a better approximation of the real shell's behavior. While the errors were higher than desired, they remained stable and within a predictable range, suggesting that the mapped model converged to reality with an offset caused by factors such as simulation approximations or data quality from the stamping process. This work highlights that predicting the plastic behavior of a hardened component using a model with uniform properties is not feasible. The excessive approximations inherent in uniform models fail to capture the inhomogeneities caused by work hardening.