## 1 Introduction
### Overview of Material Models
\right., \tag{3}\]  
where \(\varepsilon_{\text{P}}\) and \(\sigma_{\text{p}}\) denote the strain and stress of \(p\) offset (with a plastic strain of \(p\)), \(E_{\text{P}}\) represents the tangent modulus at \(\sigma_{\text{P}}\) as calculated by expressions provided by the authors [5], and \(\varepsilon_{\text{eu}}\) and \(\sigma_{\text{eu}}\) are the strain and stress of the equivalent ultimate point. Similarly, [PERSON] et al. [6] developed a simple approach to modeling the stress-strain relationship of stainless steel. Their approach involves the development of two-stage models predicting stress-strain behavior covering the full range of tensile and compressive strains separately. To obtain a comprehensive stress-strain model covering the entire range of tensile and compressive strains, it is recommended to combine proposed tensile and compressive models. For the definition of the model, only [PERSON]'s modulus and the parameters of the Ramberg-Osgood monotonic equation are used. Another model, also defined using three Ramberg-Osgood parameters, is the two-stage [PERSON] model defined in [7] as:  
\[\epsilon=\left\{ \begin{array}{ll}\frac{\sigma}{E}+0.002\Big{(}\frac{\sigma}{R_{ \text{p}0.2}}\Big{)}^{n}&\text{for }\sigma\leq R_{\text{p}0.2}\\ \frac{\sigma-R_{\text{p}0.2}}{E_{0.2}}+\varepsilon_{\text{u}}\big{(}\frac{ \sigma-R_{\text{p}0.2}}{\sigma_{\text{u}}-R_{\text{p}0.2}}\Big{)}^{m}&\text{ for }\sigma>R_{\text{p}0.2}\end{array} \right., \tag{4}\]  
where \(R_{\text{p}0.2}\) is 0.2% proof stress representing equivalent yield stress, \(E_{0.2}\) is tangent modulus of the \(\sigma\)-\(\varepsilon\) curve at the yield stress, \(\sigma_{\text{u}}\) is ultimate tensile strength, and \(m\) is the coefficient determining the shape of the second stage of the curve, which can be calculated with an accompanying equation specified by the author [7] requiring only \(R_{\text{p}0.2}\) and \(\sigma_{\text{u}}\). As opposed to the aforementioned models, complex constitutive material models enable a more comprehensive modeling of mechanical behavior of components under cyclic loading conditions, including phenomena such as the Bauschinger effect and ratcheting. Among these models, the Chaboche material model [8] is frequently used [9; 10]. This model accounts for isotropic and kinematic hardening or softening behavior, reflecting changes in the yield surface throughout loading cycles. In contrast to models based on the Ramberg-Osgood material model, which need fewer parameters for their definition, the Chaboche model incorporates additional parameters to accommodate a broader range of material behaviors [10]. However, obtaining material parameters necessary for defining the Chaboche model is not always straightforward, requiring the additional experimental characterization of material behavior, including tensile and cyclic tests. Therefore, in situations wherein simplicity and computational efficiency take priority over capturing intricate material behaviors, models like those based on the Ramberg-Osgood model may be preferable. In cases wherein those models suffice, they can be represented within finite element analysis using a multilinear material model. When formulating the multilinear material model in some commercially available finite element analysis software, whether based on one of the mentioned material models or another tailored to a specific material group or loading condition, the calculation of stress values is conducted for specific plastic strain values. The elastic strain is determined using Young's modulus and Poisson's ratio. Figure 1 provides an illustrative example of a multilinear curve, defined by five combinations of stress and plastic strain values for incremental selection of stress values in equal steps. The computation of plastic strain values is then performed for each specific stress increment, with the first point conventionally having the stress value equal to yield stress, \(R_{\text{e}}\), or some other designated stress value.