## Appendix A  
This section describes the regression used to determine the parameters \(c\) and \(d\) for the power approach described in Section 3.4.2. As shown in Figure 8, when \(\log(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/E)\) is plotted against \(\log(\Delta\sigma_{\text{el,FEA}})\) using a double logarithmic scale, the curve can be described using a linear scale for \(\log(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/E)\geq-4\). For the linear regression, the logarithm of Equation (A1) and the support points from the FEA are used; see Equation (A2). The substitutions in Equations (A3)-(A6) result in a linear equation in the form of Equation (A7).  
\[\Delta\varepsilon_{\text{P}}(\Delta\sigma_{\text{el}})=\frac{\Delta\sigma_{ \text{el}}}{E}+2\left(\frac{\Delta\sigma_{\text{el}}}{2\cdot c}\right)^{\frac{ 1}{2}}\] (A1)\[\log\biggl{(}\Delta\varepsilon_{\text{FEA}}-\frac{\Delta\sigma_{\text{el,FEA}}}{ \text{E}}\biggr{)}=\frac{1}{\text{d}}\cdot\log(\Delta\sigma_{\text{el,FEA}})- \frac{1}{\text{d}}\cdot\log(2\cdot\text{c})+\log(2) \tag{10}\]  
\[\text{y}=\log\biggl{(}\Delta\varepsilon_{\text{FEA}}-\frac{\Delta\sigma_{\text{el, FEA}}}{\text{E}}\biggr{)} \tag{11}\]  
\[\text{a}=\frac{1}{\text{d}} \tag{12}\]  
\[\text{x}=\log(\Delta\sigma_{\text{el,FEA}}) \tag{13}\]  
\[\text{b}=-\frac{1}{\text{d}}\cdot\log(2\cdot\text{c})+\log(2) \tag{14}\]  
\[\text{y}=\text{a}\cdot\text{x}+\text{b} \tag{15}\]  
The parameters a and b are obtained by the method of least squares using Equations (12) and (13) and n pairs of values x and y:  
\[\text{a}= \frac{\text{n}\cdot\sum_{i=1}^{n}\text{x}_{i}\cdot\text{y}_{i}- \sum_{i=1}^{n}\text{x}_{i}\cdot\sum_{i=1}^{n}\text{y}_{i}}{\text{n}\cdot\sum_ {i=1}^{n}\text{x}_{i}^{2}-\left(\sum_{i=1}^{n}\text{x}_{i}\right)^{2}} \tag{16}\]  
\[\text{b}= \frac{\sum_{i=1}^{n}\text{x}_{i}^{2}\cdot\sum_{i=1}^{n}\text{y}_{i}- \sum_{i=1}^{n}\text{x}_{i}\cdot\sum_{i=1}^{n}\text{x}_{i}\cdot\text{y}_{i}}{ \text{n}\cdot\sum_{i=1}^{n}\text{x}_{i}^{2}-\left(\sum_{i=1}^{n}\text{x}_{i} \right)^{2}} \tag{17}\]  
The parameters c and d are obtained by transforming Equations (12) and (14):  
\[\text{d}= \frac{1}{\text{a}} \tag{18}\]  
\[\text{c}= \frac{1}{2}\cdot 10^{\frac{1}{4}\cdot(\log(2)-\text{b})} \tag{19}\]  
In the regression, only pairs of values from \(\Delta\sigma_{\text{el,FEA}}\) and \(\Delta\varepsilon_{\text{FEA}}\) from FEA that fulfil the condition \(\log(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/\text{E}) \geq-4\) are considered. In the case that less than two load steps are necessary to perform a linear regression to fulfil the condition \(\log(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/\text{E}) \geq-4\), all load steps for which \(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/\text{E}>0\) are used. This last restriction is necessary because in the range of low loads, a negative difference \(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/\text{E}\) can occur due to numerical inaccuracies during the FEA. Since the logarithm can only be applied to values greater than zero, only data pairs for which \(\Delta\varepsilon_{\text{FEA}}-\Delta\sigma_{\text{el,FEA}}/\text{E}>0\) applies are considered.