## 4 Discussion
### Dual Loading Cases
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loading Conditions** & **TL** & **TR** & **BL** & **BR** \\ \hline Shear + Compression (SC) & 0.3050 (O) & 0.0040 (O) & 0.0048 (O) & 0.311 (O) \\ \hline Shear + Bending (SB) & 0.0191 (O) & 0.0008 (O) & 0.0950 (X) & 0.287 (O) \\ \hline Compression + Bending (CB) & 0.0445 (O) & 0.3290 (O) & 0.2660 (O) & 0.218 (O) \\ \hline \hline \end{tabular} Note: (X) denotes fracture, and (O) denotes safety.  
\end{table} 
Table 7: The largest equivalent plastic strain values for the critical elements under the dual loading cases. Figure 9: Stress triaxiality vs. equivalent plastic strain diagram for the dual loading cases: (**a**) shear and compression, (**b**) shear and bending, and (**c**) compression and bending. conditions. Compressive loading resulted in a similar deformation path for all corners with significant plastic strain but no fracture. Under dual loading conditions, compressive loading combined with other loadings changed the critical location and resulted in larger plastic strain. However, the compressive load suppressed fracture by shifting the stress triaxiality in a negative direction. Under complex loading conditions, the position of large plastic strain differed significantly. Hence, this work highlights the importance of the path change of inelastic deformation under different mechanical loading conditions. Based on the results, this study plans some future works. First, by accounting for the IMC and PCB as deformable bodies, it plans to conduct a more detailed study. For this purpose, experimental verification of the inelastic properties of IMC and PCB will be conducted. Subsequently, DIC (Digital Image Correlation) can be employed to develop an advanced model, considering the strain rate effect with more diverse external force conditions, which will enable more accurate predictions as part of our future work. Furthermore, upon obtaining images of the solder's microstructure before and after deformation, microscale analysis through CP and DD interpretations would also be feasible. Conceptualization, E.-H.L. ; methodology, J.-H.L., D.-H.L. and E.-H.L. ; software, J.-H.L. and D.-H.L. ; validation, J.-H.L. and D.-H.L. ; formal analysis, J.-H.L., D.-H.L. and E.-H.L. ; investigation, J.-H.L. and D.-H.L. ; resources, E.-H.L. ; data curation, J.-H.L. and D.-H.L. ; writing--original draft preparation, D.-H.L. ; writing--review and editing, J.-H.L. and E.-H.L. ; visualization, J.-H.L. and D.-H.L. ; supervision, E.-H.L. ; project administration, E.-H.L. ; funding acquisition, E.-H.L. All authors have read and agreed to the published version of the manuscript. This work was partially supported by the Korea Institute for Advancement of Technology (KIAT) grant (P0008458, HRD Program for Industrial Innovation) funded from the Ministry of Trade, Industry & Energy (MOTIE, Korea), and the Technology Innovation Program (Public-private joint investment semiconductor R&D program (K-CHIPS) to foster high-quality human resources) (RS-2023-00236091, Hybrid bonding technologies for 3D package interconnects). Not applicable. Data are contained within the article. The authors declare that there are no conflict of interest.