## 2 Materials and Methods
### Virtual Dataset under Investigation
For consideration of failure in the numerical simulations, the failure model generalized incremental stress-state dependent damage model (GISSMO) was applied within this work. It allows incremental damage accumulation and defining an arbitrary triaxiality-dependent failure strain; the latter is the input of the material model. GISSMO permits an incremental description of damage accumulation, including softening and failure, and provides the advantage of specifying an arbitrary triaxiality-dependent failure strain. The incremental damage accumulation is defined by [28; 29; 31; 33]:  
\[\dot{D}=\frac{n}{\epsilon_{f}}D^{(1-\frac{1}{n})}\dot{e_{p}}. \tag{10}\]  
Here, \(D\) represents the current value of damage, \(\dot{e_{p}}\) is the plastic strain rate, \(n\) is the damage exponent, and \(\epsilon_{f}\) is the equivalent plastic strain at failure. The forming intensity parameter F takes into account the onset of necking. \[\sigma_{vm}=\sqrt{\frac{3}{2}[(\sigma_{xx}+p)^{2}+(\sigma_{yy}+p)^{2}+(\sigma_{ zz}+p)^{2}+2\sigma_{xy}^{2}+2\sigma_{yz}^{2}+2\sigma_{xz}^{2}]}. \tag{2}\]0and the critical strain curve \(\epsilon_{crit}(\eta)\) is also a function of the triaxiality for coupling damage and stress under proportional loading. The functions \(D\) and \(F\) primarily differ in the type of limiting strain, which depends on the applied triaxiality forms \(\epsilon_{f}\) or \(\epsilon_{crit}(\eta)\). Within this formulation, the damage is coupled to the stress tensor. By applying the concept of effective stress of [PERSON] [34; 35], once instability is reached, \(F=1\). \[\sigma_{vm}=\sqrt{\frac{3}{2}[(\sigma_{xx}+p)^{2}+(\sigma_{yy}+p)^{2}+(\sigma_{ zz}+p)^{2}+2\sigma_{xy}^{2}+2\sigma_{yz}^{2}+2\sigma_{xz}^{2}]}. \tag{2}\]1  
Here, \(D_{crit}\) represents an indicator for reaching the onset of necking. The fading exponent \(m\) is used for the regularization of fracture strain and the energy consumed during post-instability deformation [29]. For more detailed information on GISSMO, please refer to [29]. In several material cards, and so in MAT_187_SAMP-1, there exists the possibility to import experimental data directly as a defined curve or a table. Since these experimentally measured data usually do not lead to the desired agreement or sometimes cannot even be measured completely, the material card input curves (MCIC) are parameterized by a mathematical formulation, and subsequently their parameters are calibrated in an optimization or trial-and-error process. Thus, the MP to be determined are the parameters of the mathematical formulation and therefore are only included indirectly into the material card. In the following, the formulation of the input consisting of parameters and curves used in this work is briefly presented. This is adapted from the work in [7], but the 19 material parameters used were reduced by the bulk modulus, since this exerts no influence on the used shell models. In the present work, the yield curve formula of [PERSON] et. al [26] with a combination of second-degree polynomial and root function was used:  
\[\sigma_{vm}=\sqrt{\frac{3}{2}[(\sigma_{xx}+p)^{2}+(\sigma_{yy}+p)^{2}+(\sigma_{ zz}+p)^{2}+2\sigma_{xy}^{2}+2\sigma_{yz}^{2}+2\sigma_{xz}^{2}]}. \tag{2}\]2  
with \(a\), \(b\), \(c\), and \(d\) representing the material parameters and \(\epsilon_{pl}\) the plastic strain. The relationship of the PPR as a function of plastic strain in uniaxial tension, and compression is described with the following formula:  
\[\sigma_{vm}=\sqrt{\frac{3}{2}[(\sigma_{xx}+p)^{2}+(\sigma_{yy}+p)^{2}+(\sigma_{ zz}+p)^{2}+2\sigma_{xy}^{2}+2\sigma_{yz}^{2}+2\sigma_{xz}^{2}]}. \tag{2}\]3  
with \(\upsilon_{p}\) being the plastic Poisson's ratio. The formula describes an exponential decay from the constant PPR \(\upsilon_{p,press}\) of the compression side to a plateau on the tension side. Here, \(\upsilon_{p,plat}\) is the respective PPR value of the tension side and \(\epsilon_{p,plat}\) defines the value where 99% of the difference between compression and tension is subtracted.