# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 8 Conclusions and Outlook  
The MPM is an efficient, stable, and easily implementable new approach that has received widespread attention in the field of computational mechanics since its inception. Through continuous research and development by scholars at home and abroad, the MPM has been widely applied in various fields and has yielded a multitude of research outcomes. This article provides a systematic review of the advancements in the MPM and its diverse coupling schemes as applied to scenarios like high-speed impact, explosion, dynamic cracking, impact penetration, and FSI. Table 1 summarizes the main variants and developmental history of MPM, while Table 2 further outlines the strengths and weaknesses of the MPM in these large deformation application areas. Although the MPM has achieved significant development, future attention and in-depth research are still needed in the following areas:  
1. Enhancing the computational efficiency of the MPM. Current developments in the MPM are primarily based on explicit time integration; although implicit integration schemes can improve the computational efficiency of the MPM in large deformation analysis, the computational cost can significantly increase when dealing with large-scale physical problems. Therefore, future research could focus on optimizing the distribution and quantity of material points, developing a three-dimensional MPM computational architecture with GPU parallel acceleration, and exploring intelligent MPM computation methods combined with neural networks. 2. Addressing the grid dependency of the MPM. Similarly to the FEM, the simulation results of the MPM are highly dependent on the background grid used, and in cases where strain localization phenomena are significant, pathological grid dependency may occur. Therefore, generating an appropriate grid is a time-consuming and challenging task, especially when dealing with problems of complex shapes and moving boundaries. It is recommended to introduce non-local grid regularization methods, dynamic grid methods, and overlapping grid methods to obtain objective and stable MPM solutions. Figure 26: Collision detection between the MPM and SDEM [120]. 3. Refining boundary detection algorithms. In MPM computations, even when using a fixed background grid, grid nodes may not coincide perfectly with domain boundaries, which can lead to inaccurate boundary representation. Thus, the use of machine learning-assisted detection can be considered, such as employing CNNs to identify boundary features. 4. Expanding the MPM's multi-field coupling capabilities. While enhancing MPM's mechanical computation capabilities, it is essential to further expand the application scope of this method in multi-physical field problems, leveraging the MPM's advantages in solving other physical fields such as heat transfer and electromagnetism. This will significantly promote the resolution of the complex engineering computation problems currently being faced. 5. In the field of fluid dynamics, there is a need to develop an efficient MPM coupling algorithm that can accurately solve problems involving highly compressible fluids, as well as to develop an MPM model capable of simulating high-viscosity non-Newtonian fluids.