# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 1 Introduction  
With the rapid development of computer technology, numerical simulation techniques have been widely applied in engineering and scientific research. Common numerical computation methods are generally categorized based on the continuity of the problems they solve into continuous mechanics computation methods and discontinuous mechanics computation methods. The former is typically suitable for solving solid or fluid mechanics scenarios that are described by systems of partial differential equations as a whole, including the finite difference method [1], finite element method [2], finite volume method [3], boundary element method [4], and meshless method [5]; the latter focuses on solving problems involving flow, cracking, large deformation, and other behaviors in block or granular materials, including the discrete element method [6] and discontinuous deformationanalysis [7]. Since actual engineering often involves multiphase media, and each material exhibits complex mechanical behaviors such as irregular boundaries, nonlinear constitutive relations, large deformations, cracking, and even fragmentation, scholars have been seeking efficient computation methods beyond continuous and discontinuous mechanics, such as coupled continuous-discontinuous computation models [8; 9]. The finite difference method (FDM) primarily employs an Eulerian description, which, while free from grid distortion issues, encounters difficulties with complex geometric shapes, boundary handling, and challenging interface tracking. The finite element method (FEM) and other Lagrangian methods face grid distortion when dealing with large strain problems. Employing erosion algorithms to delete distorted grids can lead to the non-conservation of system mass, while grid re-meshing results in the loss of historical information and increased computational demands. To address the myriad issues associated with grid-based methods, the meshless method emerged. It originated from the smoothed-particle hydrodynamics (SPH) method proposed by [PERSON] [10], which, although unaffected by grid characteristics and suitable for handling large deformations, still faces issues such as low computational efficiency, complex contact algorithms, and difficult boundary condition handling. In this context, the material point method (MPM) has garnered significant attention due to its advantages in easily handling large deformations, no particle interface crossing, and high computational efficiency. The MPM traces its origins back to the particle-in-cell (PIC) method proposed by [PERSON] [11], which was initially applied to fluid dynamics. To address the numerical dissipation issues encountered in PIC, [PERSON] et al. [12] developed the fluid implicit particle (FLIP) method based on PIC. In 1994, to extend FLIP to the field of solid mechanics and to resolve the high numerical dissipation problems in PIC, [PERSON] [13] optimized FLIP and termed it the MPM. The MPM was first validated for its significant advantages in handling large deformation problems through simulations of rigid body rotation and elastic body collision. Subsequently, the MPM has been widely applied and rapidly developed in the field of computational mechanics. This paper systematically summarizes the applications of the MPM in high-speed impact, explosion, dynamic cracking, impact penetration, and fluid-structure interaction problems, analyzing the unparalleled advantages of this method in dealing with extreme deformation issues.