## 1 Introduction  
The incremental forming process is a relatively new process that is constantly being developed and improved and is being used in more and more industrial fields, especially in those involving the production of parts in small series, prototypes or one-off productions. In contrast to traditional forming processes, where the active element (in most cases, the punch) only performs an alternating rectilinear movement to produce the part,the incremental forming process produces a complex, three-dimensional trajectory. The main advantage consists in the universality of the process, allowing for a wide variety of geometric shapes to be produced using the same punch and die but with different trajectories. In recent years, interest in the incremental forming of polymeric materials has grown significantly, driven by their extensive industrial applications and the rising demand for prototypes, one-off components, and small-batch production. The automotive sector, in particular, has been actively exploring the replacement of metal components with lighter alternatives to reduce vehicle weight and enhance fuel efficiency and autonomy [1]. Furthermore, the biocompatibility of specific polymeric materials with human tissue has enabled the use of incremental forming techniques for the fabrication of biomedical implants. These implants, often derived from autologous or cadaveric sources, aim to reduce immunological rejection and minimize the risk of postoperative infection [2; 3]. The latest advances in incremental forming of polymeric materials were presented by [PERSON] et al. [4]. Most papers published on this topic study the formability of polymeric materials [5], as well as the variation of main strains and thickness reduction [6] and forces occurring in the forming process [7]. Polycarbonate materials [8] and polypropylene materials [9] are the most frequently studied materials in the scientific literature. Regarding numerical simulation, using the finite element method of an incremental forming process, most papers have studied the behaviour of metallic materials. A synthesis paper offers a comprehensive analysis of the use of the finite element method (FEM) in modelling the incremental forming of metal sheets [10]. The authors provide an overview of the evolution of the finite element method (FEM), discussing the different types of simulations employed and the commonly used software platforms, including Abaqus, Ls-Dyna, and Ansys. They highlight the benefits of FEM in incremental forming, such as precise prediction of stress and strain distribution, force dynamics, and material thinning. The study underscores the critical role of FEM simulations in process optimization, cost reduction, and enhancing the quality of the final components. Incremental forming of metal sheets by methods, with and without the use of auxiliary tools, using finite element method (FEM) simulations is analysed by [PERSON] [11]. Finite element method (FEM) simulations revealed notable distinctions between single-point incremental forming (SPIF) and two-point incremental forming (TPIF), emphasising the positive impact of auxiliary tools on enhancing geometric precision and forming consistency. The study offers a strong foundation for optimising incremental forming process and underscores the advantages of incorporating auxiliary tools to achieve higher-quality components. [PERSON] et al. developed a thermomechanical model in Abaqus incorporating the damage initiation criteria to simulate the behaviour of long fibre-reinforced composite materials at forming temperatures around 220 \({}^{\circ}\)C [12]. To enhance formability, they introduced an innovative setup featuring controlled hydrostatic pressure and a protective AA-6056 aluminium alloy sheet. The study examined the effects of laminate configuration, applied pressure, and tool path strategy on the quality of the formed components. Results indicated that hydrostatic pressure and alternating tool paths significantly reduce thinning and enhance geometric precision. [PERSON] et al.