## 2 Simulation of Roller Hemming
### Establish Model of Simulation  
Commercial finite element software, DEFORM ver. 11.0, for sheet metal forming was utilized to simulate the roller hemming process. Finite element analysis (FEM) was employed for two reasons. On the one hand, this approach can flexibly adjust the process parameters of the rolled edge and subsequently simulate and analyze rolled edge forming under different process parameters in a relatively short period, which increases its efficiency and saves time. Notably, this also eliminates the costly trial-and-error approach that is traditionally used for the quality debugging of rolled edges. On the other hand, finite element analysis reduces the labor and material consumption associated with this traditional process. The results of the FEM numerical analysis were utilized to optimize the geometric process parameters. Technical standards for roller hemming process parameters were established. This in turn ensured that high-quality results could be achieved more efficiently and at a reduced cost. True stress-true strain is solely relevant for uniform deformation. In the process of inputting material data into DEFORM, we define the range from the lower yield point to the tensile strength (maximum load point) as exhibiting uniform deformation. Subsequently, stress-strain data for this deformation are integrated into the DEFORM pre-processing material library, after the acquisition of the material properties from Figure 1b. Figure 1: Tensile testing machine was employed to obtain stress and strain data from a hot-dip galvanized steel panel (the SGCC grade of JJSG 3302), offering valuable insights into the material’s behavior under tension. Nominal stress–strain and true stress–strain data are represented by the black curved line and the red curved line, respectively. (**a**) A tensile testing machine. (**b**) The curve figure of strain-stress. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Yield Point** & **Tensile Strength** & **Elastic Modulus** & **Poisson’s Ration** \\  & **[MPa]** & **[MPa]** & **[GPa]** & \\ \hline SGCC & 300 & 412.43 & 210 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties of SGCC. As shown in Table 4, the model used in DEFORM was employed to simulate the roller hemming process. The simulation encompassed both straight-edge and curved-edge flat surfaces, as these two parts are integral to both simulation and experimental setups. The entire model was created in a three-dimensional (3D) framework using the Lagrangian incremental method and a sparse solver to enhance computational efficiency. The Newton-Raphson iteration method was selected to ensure convergence of the calculation results. The roller and die were treated as rigid bodies, while the door panel was modeled as an elastic-plastic body using a tetrahedral element. The tetrahedral element compared to shell elements accounted for both node rotation and torsion. This allowed for a more accurate representation of the interaction forces and the deformation behavior of the entire door panel during the roller hemming process. The mesh grid size for the entire door panel area was set at 0.3 mm, resulting in a total of 200,000 finite elements. Considering the smoothness of both the panel and the roller surfaces, the roller was assumed to rotate frictionlessly along its axis of revolution. A shear friction coefficient and a normal Coulomb friction coefficient of 0.13 were applied between the panel, roller, and die [23]. The contact settings for the simulation process in both straight-edge and curved-edge were as follows: During the flange step, the die, panel, and holder were set to face contact, with no relative movement. In the pre-hemming and final-hemming steps, the roller was configured to rotate along its axis parallel to the length of the panel, while the panel maintained face contact with the die. Additionally, the non-deformed surface on the exterior of the panel was designated as a symmetric surface.