### Numerical Forming Force Prediction  
In the case of ISF simulations, the incremental forming toolpath adds further complications to the typical sources of nonlinear behavior encountered in conventional forming processes, such as plasticity, large strain effects, and contact. Therefore, even for the simulation of straightforward parts, solution times of days or weeks have been reported [21]. Different approaches have been proposed to alleviate the lengthy numerical solution process. Researchers using implicit solvers implemented numerical strategies like substructuring [22], submodeling [23], adaptive remeshing [24], or simplified contact algorithms [25]. Others relied on explicit time integration solvers with an increase in the minimum time step by using either mass scaling, tool velocity scaling, or a combination of the two [26]. The predictive capability of Finite Element Method (FEM) simulations depends on several parameters, including the type of results being analyzed. For example, [PERSON] et al. [27] achieved a precise geometric description of their part fabricated with low-carbon steel DC04. Conversely, force estimations for aluminum alloys have been reported to deviate by up to 30% from experimental results [28; 29]. The axial force overestimation has been primarily linked to the choice of the element types and material constitutive models. Regarding spatial discretization, researchers have employed both continuum and shell elements [23; 30]. Partial models based on continuum elements allowed the discovery of the through-thickness shear in SPIF, later confirmed by experimental results [31]. Nevertheless, simulating full-scale parts using continuum elements remains a computationally challenging task, leading to the prevalent use of shell elements in global models. The constitutive material model for sheet metal forming simulations comprises a flow rule, a yield criterion, and a hardening law [32]. Metallic elastoplastic material models available in most commercial FEM codes are based on the associated flow rule. It has been demonstrated that anisotropic yield models have a minimal impact on the computation of strain for SPIF simulations [33; 34; 30]. Anisotropy parameters are typically determined from uniaxial tensile tests, generally limited to low plastic strain levels. However, during the SPIF process, the material undergoes substantial plastic deformation, often exceeding 50%. In such cases, it may be necessary to incorporate anisotropic yield surfaces that evolve with plastic strain increments. [PERSON] et al. [35] demonstrated this by employing a sixth-order polynomial yield surface, considering the evolution of the sheet anisotropy during an oval hole expansion test. Notably, the yield surface parameter determined under large strain conditions successfully predicted the direction of fracture onset in the material. For the moment, the implementation of the von Mises yield model is the common practice in the simulation of ISF. As for the hardening law, most works have relied on isotropic hardening models. Specifically, an exponential law with either two, Hollomon  
\[\sigma=K\epsilon^{n} \tag{5}\]  
or three parameters, Swift  
\[\sigma=K(\epsilon_{0}+\epsilon_{P})^{n} \tag{6}\]has been used. Additionally, the Voce law has been applied to describe the stress saturation shown by some aluminum alloys as  
\[\sigma=A-B\mathrm{e}^{-C\varepsilon_{P}}. \tag{7}\]  
In Equations (5)-(7), \(\varepsilon_{0}\) is the strain at yield, \(\varepsilon_{p}\) is the plastic strain, and \(K\), \(n\), \(A\), \(B\), and \(C\) are parameters identified from tensile test data. [PERSON] et al. [34] studied several numerical parameters when comparing the force predictions from different simulation setups to experimental results of conical frusta formed with AA3003-0. The authors concluded that the best estimations were achieved with a combination of continuum elements, a refined mesh sub-model, and a mixed isotropic-kinematic hardening model adjusted with an inverse simulation of the linear indentation test. [PERSON] et al.