## 1 Introduction
Complex material behavior, extensive sliding contact between tools and metal sheets and large deformations define all the processes. These aspects mean that the numerical approach of the process is complicated. One of the first studies on the springback of sheet metal forming carried out by finite element analysis was performed by [PERSON] et al. [11]. Numerical results and experimental results reached a very good agreement for simple geometries, which are achieved by using commercially available models. The model is built with shell elements with an implicit time integration scheme. To handle contact within rigid and deformables bodies, a penalty method algorithm was implemented. [PERSON] and [PERSON] [12] set up a scenario where both explicit and implicit methods are banded together. The explicit method has been used to reproduce the process, while the implicit method has only been used during the springback phase. [PERSON] et al. [2] dealt with a large deformation algorithm to analyze the modeling of a bending process of a metal sheet by simulation and showed that the results agree with the experimental test. Thus, in the early stages of springback numerical simulation, the main contributions were focused on developing the best FEM approach to simulate the process. However, although the accuracy of the results was promising, there was room for improvement. So, in recent years, the mathematical modeling of constitutive laws of materials has received a lot of attention. Due to the cold-rolling process, the materials used in forming manufacturing are generally orthotropic. Moreover, austenitic steels' final material properties depend on the actual austenitic and martensitic composition that evolves with the deformation of the material. This is because the phase transformation results in different hardening curves for different stress states. Strain-dependent hardening and plastic anisotropy are studied in [13]. Complex shapes of the dies cause the metal to flow through them to bend in one direction and then rebend in the opposite direction. This behavior under loading and unloading conditions, driven by the Bauschinger effect [14], has a great impact on the resulting stress states at the end of the forming process. The Bauschinger effect refers to the phenomenon where a material that has been plastically deformed in one direction exhibits a reduced yield stress upon loading in the reverse direction. In a recent study, a physically based self-consistent model was developed to examine the microscopic lattice response of pre-strained Type 316H polycrystalline austenitic stainless steel and to explain the Bauschinger effect observed at the macroscopic scale [15]. This effect is fundamentally attributed to changes in the internal structure of the steel induced by the initial deformation. Microscopically, plastic deformation creates an inhomogeneous distribution of residual stresses and dislocation structures inside the material. These internal stress fields act as back-stresses that facilitate dislocation motion when the load is reversed. As a result, upon load reversal, the pre-existing dislocation arrangements and residual stresses reduce the resistance to plastic flow, causing early yielding in the opposite direction. This manifests as a drop in the yield point on the reverse stress-strain curve compared to the initial direction. [PERSON] [16] considered a U-channel stamping analysis to anticipate springback deformations. Kinematic hardening is modeled, maintaining the dimension of the primary yield surface and moving this surface. The location of the center of the initial yield surface is the back-stress. He developed a kinematic hardening model with a cumulative back-stress. [PERSON] and [PERSON] [17] demonstrate the grade of implication of the Bauschinger effect on springback with an experimental edge bending trial.