## 4 Conclusions  
The analysis of the information presented in this paper leads to the following main conclusions:  
* Finite element simulation of the incremental forming process for polymeric materials yields results that closely align with experimental data, demonstrating strong agreement in both the distribution and magnitude of strain and thickness reduction. * The force variation curves obtained through finite element simulation closely match the experimental results, with only minor discrepancies observed between the numerical and experimental values. * To achieve higher accuracy in simulating the incremental forming process, material model 24 in Ls-Dyna is recommended for polyamide and model 89 is recommended for polyethylene when predicting specific strains and thickness reduction. However, for more accurate force prediction during the forming process, material model 89 is recommended for both polymer types. * When the appropriate material model is applied, the discrepancy between experimental and simulated results for specific strains and thickness reduction (excluding minor strain) remains within a maximum of 2.55% for polyamide and 4.21% for polyethylene. * Using the appropriate material model, the maximum deviation between experimental and simulated process forces is 2.54% for polyamide and 2.71% for polyethylene, respectively. It can be concluded that, despite the computational intensity and sensitivity to various parameters, the simulation of the incremental forming process can yield highly accurate results--provided that optimal input conditions are ensured, including appropriate finite element mesh density, suitable material models, and accurately defined contact interactions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Material Type**} & \multicolumn{1}{c}{**Material Model**} & \multicolumn{1}{c}{**F\({}_{\rm z}\) Force**} & \multicolumn{1}{c}{**F\({}_{\rm x}\) Force**} & \multicolumn{1}{c}{**F\({}_{\rm y}\) Force**} \\  & & **[\%]** & **[\%]** & **[\%]** \\ \hline \multirow{2}{*}{PA} & 24 & 4.23 & 4.74 & 4.56 \\ \cline{2-5}  & 89 & 1.83 & 2.24 & 2.54 \\ \hline \multirow{2}{*}{PE} & 24 & 4.78 & 4.68 & 4.30 \\ \cline{2-5}  & 89 & 2.43 & 2.71 & 2.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Force differences between experimental and simulated values for polyamide and polyethylene. The inclusion of strain rate effects can lead to an improvement in the quality of the results in most FEM simulations of forming processes. We did not take this effect into account because the single-point incremental forming process is a slow, quasi-static process, especially if an industrial robot is used, as in our case. The vast majority of other studies regarding FEM simulation of the behaviour of polymeric materials during single-point incremental forming refer only to the analysis of the results obtained and their comparison with experimental results. In contrast, the study presented in this paper is the first to constitute a practical tool for choosing the closest material model for two types of polymeric materials (PA 6.6 and PEHD) depending on the accuracy of simulations related to forces or strains. In future research, we will aim to perform FEM simulations using material models with viscoelastic or hyperelastic behaviour to increase the accuracy of the obtained results. Conceptualization, N.R., T.T., E.A. and M.O. ; methodology, N.R., E.A., S.M.N. and V.O. ; software, N.R., S.M.N., M.O. and E.A. ; validation, S.M.N., T.T. and V.O. ; formal analysis, N.R., E.A. and M.O. ; investigation, N.R., M.O., E.A. and V.O. ; resources, E.A., M.O., T.T. and S.M.N. ; data curation, V.O., T.T. and S.M.N. ; writing--original draft preparation, N.R, T.T., S.M.N. and M.O. ; writing--review and editing, S.M.N., E.A., T.T. ; visualization, N.R., V.O. ; supervision, T.T., S.M.N. and V.O. ; project administration, E.A. and M.O. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.