## 1 Introduction
Two constitutive models, one based on a hyperelastic-plastic constitutive equation and another based on a simplified semi-analytical model that extends the specific energy concept used in materials processing, are used to predict forming forces at SPIF process [18]. Both methods were experimentally validated using polycarbonate (PC) and polyvinyl chloride (PVC) sheets, showing strong correlation with the observed results. The FEM model effectively predicted temperature distribution and material thickness throughout the forming process. The occurrence of wrinkling defects in the SPIF process of thin polycarbonate sheets is investigated through a combination of experimental tests and finite element method simulations [19]. The study examines how tool path parameters--specifically wall angle and vertical step--affect forming forces, strain distribution, and thickness reduction. Findings reveal that these process parameters play a critical role in the onset of wrinkling and twisting, underscoring their impact on the overall quality of the SPIF process. [PERSON] et al. developed a coupled thermomechanical numerical model to simulate the SPIF process with convective heat assistance for polycarbonate sheets [20]. The model incorporates a spatial distribution of convective heat transfer coefficients to replicate localized heating and employs the temperature dependent Three-Network Model (TNM) within the Ansys simulation software. The approach was applied to the forming of a frustum of a cone with a 45\({}^{\circ}\) wall angle. Experimental validation demonstrated strong agreement, with a temperature prediction error of \(\pm\)5 \({}^{\circ}\)C and a displacement deviation of approximately 0.77 mm. The optimization of the SPIF process applied to polycarbonate sheets, using finite element method (FEM) simulations, is analysed by [PERSON] et al. [21]. The study explored how different tool path strategies affect forming forces, deformation behaviour, energy consumption, and processing time in the SPIF process. The findings revealed that employing alternating tool paths--combining ascending diagonal and descending vertical steps--significantly reduces forming forces and minimizes defects such as wrinkling and sheet twisting. This strategy enhances surface finish and lowers energy usage while maintaining efficient production times. Having reviewed the research in this field, the present paper aims, by means of a comparative study, to analyse the differences obtained between numerical simulation and experimental research for two material models from the Ls-Dyna program, namely models 24 (Piecewise Linear Plasticity) and 89 (Plasticity Polymer), applied to the incremental forming process for two materials, polyamide PA 6.6 and polyethylene HDPE 1000. Both the results of the experimental investigations and the results of the numerical simulations were focused on the main strains and forces during the single-point incremental forming process. This study contributes to strengthening science, engineering, and technological development by addressing a practical yet underexplored challenge in modern simulations of forming processes: choosing the appropriate material model depending on the objective of the FEM simulation, predicting with the highest possible degree of accuracy the forces in the process, or the strain evolution during the forming process.