## 2 Simulation of Roller Hemming  
### Pre-Simulation Material Preparation  
In this research, the SGCC grade of the JISG 3302 standard refers to an automobile hot-dip galvanized steel pane, whose chemical composition is shown in Table 1. To obtain the mechanical properties required for finite element model development, tensile tests were conducted on the material, as depicted in Figure 1a. The experimental conditions for the tensile test are presented in Table 2, including the parameters used to measure the tensile load, as well as the width and length of the specimen, under a tensile velocity of 300 mm/min as set on the tensile machine. Subsequently, based on the stress-strain relationship introduced by [PERSON] and [PERSON], [21] these data were utilized in Equations (1) and (2) to derive the nominal stress-strain values. Next, Equations(1) and (2) were integrated into Equations (3) and (4) to obtain the true stress-strain results. Finally, the stress-strain curve relationship was plotted, as depicted in Figure 1b.  
\[\sigma_{n}=\frac{P}{S_{0}} \tag{1}\]  
\[\varepsilon_{n}=\frac{\Delta l}{l_{0}} \tag{2}\]  
\[\sigma_{t}=\sigma_{n}(1+\varepsilon_{n}) \tag{3}\]  
\[\varepsilon_{t}=\ln\left(1+\varepsilon_{n}\right) \tag{4}\]  
\(\sigma_{n}\): nominal stress [MPa]; \(P\): tensile load [N]; \(S_{0}\): specimen cross-sectional area [mm\({}^{2}\)]; \(\varepsilon_{n}\): nominal strain; \(\Delta l\): elongation in the length direction [mm]; \(l_{0}\): initial length [mm]; \(\sigma_{t}\): true stress [MPa]; \(\varepsilon_{t}\): true strain.  
The panel, made of hot-dip galvanized steel (the SGCC grade of JISG 3302), was subjected to tensile testing to determine its mechanical properties using a tensile testing machine (Figure 1a). As shown in Table 3, the panel sample was clamped onto the testing machine and subjected to increasing tensile force until failure. The machine recorded the applied force and the resulting deformation, allowing the calculation of key mechanical properties such as yield strength, tensile strength, modulus of elasticity, and Poisson's ratio.  
Based on the tensile curve in Figure 1b, the material's mechanical behavior closely aligns with the isotropic hardening model. Therefore, this model was applied in the simulation to represent the material's behavior. The material deformed at room temperature with uniform forming speed, neglecting strain-rate effects. As shown in Figure 1b, in the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Carbon** & **Mangenese** & **Phosphorus** & **Sulfur** \\ \hline SGCC & 0.15 & 0.8 & 0.05 & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical composition of SGCC (wt%).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equipment** & **Material** & **Width** & **Length** & **Thickness** & **Tensile Velocity** \\ \hline Tensile & & & & \\ testing & SGCC & 25 & 50 & 0.75 & 300 \\ machine & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental conditions of tensile test.  
elastic region the material followed [PERSON]'s law (Equation (5)), where \(\sigma_{e}\) represents the elastic stress (MPa), E denotes the modulus of elasticity (MPa), and \(\varepsilon\) is the strain. In the plastic region, it followed the Ludwik hardening model (Equation (6)), where \(\sigma_{p}\) is the plastic stress, \(\sigma_{y}\) is the yield strength, \(K\) is the hardening coefficient, \(\varepsilon_{p}\) is the plastic strain, and \(n\) is the hardening exponent, with the value \(n=0.2\) obtained by fitting the true stress-strain data [22].  
\[\sigma_{e}=E\cdot\varepsilon \tag{5}\]  
\[\sigma_{p}=\sigma_{y}+K\cdot\varepsilon_{p}^{n} \tag{6}\]