# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 8 Conclusions and Outlook
\begin{table}
\begin{tabular}{c c c c} \hline
**Author** & **Method** & **Key Innovations** & **Limitations** \\ \hline [PERSON] et al. (2013) [PERSON] et al. (2013) & multi-scale framework combining MD and MPM & Driving MPM macroscopic simulations with EOS data calculated from MD. & A large amount of MD state equation data needs to be precomputed. \\ \hline [PERSON] et al. (2014) ([PERSON] et al., 2014) & CFDMP & More precise treatment of explosive multi-material interfaces. & The introduction of virtual points at the interface leads to interpolation errors, which necessitate precise boundary conditions. \\ \hline [PERSON] and [PERSON] (2017) & phase-field MPM & When combined with the phase-field fracture model, explicit crack tracking is not required. & The computational workload is significantly increased. \\ \hline [PERSON] et al. (2020) [PERSON] et al. (2020) & immersed boundary MPM & Incorporating the IBM avoids the need for FSI interface reconstruction. & The introduction of virtual fluid incurs additional computational costs. \\ \hline [PERSON] et al. (2020) ([PERSON] et al., 2020) & LBMPM & Efficient simulation of large-deformation fluid–solid interaction without mesh reconstruction is achieved. & The computational efficiency in 3D is low. \\ \hline [PERSON] et al. (2020) ([PERSON] et al., 2020) & adaptive finite element material point method & Dynamically converting finite elements to material points effectively avoids mesh distortion in extreme deformation problems. & The threshold for conversion needs to be set empirically. \\ \hline [PERSON] et al. (2022) ([PERSON] et al., 2022) & adaptive peridynamics MPM & Dynamically switching between MPM and peridynamics regions enables multi-scale fracture simulation. & It requires a preset threshold for conversion. \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{The particle–surface contact model accurately simulates the entire process of rock transitioning from continuous deformation to fracture during blasting.} & The contact criterion requires iterating through all material points. \\ \hline [PERSON] and [PERSON] (2022) ([PERSON] and [PERSON], 2022) & IALEMPM & The contact criterion requires iterating through all material points. & The algorithm implementation is complex. \\ \hline \hline \multirow{3}{*}{[PERSON] et al. (2022) ([PERSON] et al., 2022) ([PERSON] et al., 2022) ([PERSON] et al., 2022)} & Incorporating weighted tracking points avoids the need for FSI interface reconstruction. & The computational cost is high, and it is difficult to apply boundary conditions. \\ \hline [PERSON] et al. (2024) ([PERSON] et al., 2024) ([PERSON] et al., 2024) & cBSMPM & Using B-spline background grids yields a smooth stress field. & Higher-order basis functions increase the computational workload. \\ \hline [PERSON] et al. (2025) ([PERSON] et al., 2025) & PF-FEMPM & Mitigate mesh-crossing instabilities. & The efficiency is lower than that of the pure MPM phase-field method. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._In summary, the further exploration of the MPM in more domains and more in-depth research and applications is warranted. This article takes the application of the MPM in handling large deformation problems as an example to organize related research, aiming to continuously deepen the theoretical connotations of this method, provide more practical basis for researchers conducting material numerical studies, and offer valuable technical references for expanding the application range of this method. Conceptualization: [PERSON]; formal analysis: Q.Z. and X.Z. ; investigation: X.Z. ; resources: C.Z. and S.C.; visualization: Q.Z. and S.C.; writing--original draft preparation: Q.Z. ; writing--review and editing: [PERSON] and S.C.; supervision: S.C.; project administration: [PERSON] and X.W. ; and funding acquisition: [PERSON] and X.W. All authors have read and agreed to the published version of the manuscript.