## 2 Materials and Methods
### Procedures
#### 2.3.2 Simulation Process  
For both drawing and trimming stages, simulation analyses were performed in Ls-Dyna/Explicit R10.1.0. The numerical model presented in Figure 9 consists of three rigid parts, the die (A), blank-holder (D), and punch (E) and one deformable body, the blank (B). The blank-holder stop (C) is a numerical tool used to model and sensor the variable blank-holder force. As described in Section 2.3.1, the simulation workflow adheres to the same manufacturing process employed for part production, as illustrated in Figure 10.  
The tool velocity, time step size, and termination time are selected in a coordinated manner. Given the total tool travel, a punch velocity profile is designed for the closing and drawing stage, as shown in Figure 11. Initially, a trapezoidal-shaped velocity is applied to  
Figure 8: Schematic set-up for the experimental springback measurement; (**A**) measuring jig; (**B**) sidewall zone for bending moments extraction  
Figure 10: Simulation process. Figure 9: Forming model: die (**A**), blank (**B**), blank-holder stop (**C**), blank holder (**D**), punch (**E**). reach the blank holder. Then, after a small acceleration, the punch operates with constant velocity until the end of the drawing process. The blank is modeled with fully integrated shell elements with nine integration points through the thickness. Due to the anisotropy of the metal sheet, some orientations have to be defined. In order to present the material properties in the different directions, a material coordinate system has to be set. The material coordinate system in each element is rotated, aligning all local material directions to the global material direction in accordance with the blank-rolling direction. For the contact within the tools and the blank, a penalty-based contact interface is employed. A friction coefficient of \(\mu=0.1\) was employed [47], reflecting the use of lubricant in conjunction with a plastic film applied to the grated side of the sheet. Under these conditions, it is observed that when \(\mu=0.1\) is assumed, the simulation yielded a stamping force that is in very close agreement with the forces measured during both the 50 t and 200 t processes. This match between the simulation and the experimental stamping force data confirms that using a constant friction coefficient is a practical and accurate simplification. A sensitivity analysis was conducted by varying the friction coefficient by \(\pm 10\%\) from the base value of 0.1. The deformation at two investigated corners showed only minor changes, remaining within acceptable tolerance limits. This low sensitivity supports the use of a constant friction coefficient in our simulations, as the key deformation characteristics and stamping force predictions remain consistent across the examined range. These results confirm that under our specific lubricated conditions, the friction coefficient does not critically alter the overall deformation behavior of the stamped part. The results of this sensitivity analysis are shown in Table 4. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \(\mu\) & **Corner** & **Deviation** & **Corner** & **Deviation** \\  & **FL** & **\%** & **FR** & **\%** \\ \hline
0.09 & \(-\)0.0814 & 4.87 & \(-\)0.2083 & 5.89 \\
0.10 & \(-\)0.0856 & & \(-\)0.2214 & \\
0.11 & \(-\)0.0902 & 6.22 & \(-\)0.2328 & 5.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sensitivity analysis results for the 200 t process, front left corner and front right corner deviation from base line friction coefficient. Figure 11: Tools velocity profile. Adaptive mesh is used to automatically subdivide elements and create refined mesh in areas of high curvature. The blank is built with a regular mesh of rectangular elements with aspect ratios as near to one as possible. The initial blank element size was set to 5 mm to accurately resolve part details.