## 4 Discussion
### Dual Loading Cases  
The deformation results of dual loading cases are shown in Figure 8. For shear and compression loading case shown in Figure 8a, the plastic strain was dominated at the TL and BR corners without fracture and was not symmetrical in either direction. In addition, there is almost no deformation at the BL corner, whereas a significant strain occurred at the TL and BR corners. This result differs from the case in which the shear loading was applied alone, where fracture occurred at the BL corner, and that in which the compressive loading was applied alone with the symmetrical strain distributions at all four corners. For the shear and bending cases shown in Figure 8b, a fracture only occurred at the BL corner. Despite a larger strain at the BR corner, no fracture was observed. A significant and dramatic change occurred where there was minimal plastic strain in the top corners. This result can be attributed to the opposing triaxiality tendencies exhibited at the TR and TL corners under each single loading condition of shear and bending, effectively compensating each other. For the compression and bending cases shown in Figure 8c, there were no fractures at all corners, and the strain at the TR corner was more than six times greater than that at the TL corner without fracture. Figure 7: Stress triaxiality vs. equivalent plastic strain diagram for the single loading cases: (**a**) shear, (**b**) compression, and (**c**) bending. Figure 9 shows the stress triaxiality and equivalent plastic strain plot for the dual loading cases. Table 7 lists the fracture strain and the largest plastic strain in the case of no fracture. For the shear and compression case shown in Figure 9a, the stress triaxiality remained in the negative region at all corners. When the solder was subjected to shear loading alone, as shown in Figure 7a, the BL and TR corners exhibited a positive triaxiality. However, for this case, the stress triaxiality value shifted significantly toward the negative side. This indicates that the combination of these two loadings leads to significant change in the deformation mode. This increased the fracture limit in areas where fractures were occurring under shear loading, so that fractures did not occur even at high plastic strain levels. The results of the shear and bending combined loading are shown in Figure 9b. As observed in Figure 8b, the plastic strain at the top corners occurred very minimally. This is because, as mentioned earlier, shear and bending generated opposing deformation paths, leading to the mutual cancellation of the inelastic deformation. Figure 8: Equivalent plastic strain contour of the dual loading cases: (**a**) shear and compression, (**b**) shear and bending, and (**c**) compression and bending. For the compression and bending case shown in Figure 9c, the effect of compression caused a significant change in the deformation path under the external bending forces, especially at the TL and BR corners. Compared to the single bending case, as shown in Figure 7c, the TL point experienced deformation in the positive triaxiality region, leading to eventual fracture. However, in the single compression loading case, the TL corner exhibited a deformation path associated with negative triaxiality, and when both external force conditions were combined, as evidenced in Figure 9c, deformation was minimal due to the offsetting effects of positive and negative triaxiality. On the other hand, the BR corner, which falls within the negative triaxiality region during bending, did not undergo significant deformation. However, it experienced a substantial increase in plastic strain levels due to compressive forces. Nonetheless, no fractures occurred in this region due to the high fracture limit associated with the negative triaxiality region.