Research Advances in Large Deformation Analysis and Applications of the Material Point Method

Large deformation analysis is a crucial foundation for studying the nonlinear behavior and progressive damage of materials and structures. Traditional mesh methods often struggle with large-scale mesh distortion when dealing with such issues, which can compromise solution efficiency and accuracy, and in severe cases, even cause computational interruptions. In contrast, the material point method (MPM) employs a dual framework of Lagrangian particles and Eulerian background grids, effectively integrating the advantages of both Lagrangian and Eulerian approaches, thus avoiding mesh distortion and challenges in handling convective terms. Consequently, many researchers are dedicated to developing an MPM for addressing high-speed impact and fluid–structure interaction problems that involve material failure and large deformations. This paper begins by introducing the fundamental theory and contact algorithms of the MPM. It then systematically summarizes the latest advancements and applications of the MPM, including its hybridization and coupling with other algorithms, in simulating various large deformation scenarios such as high-speed impacts, explosions, dynamic cracking, penetration, and fluid–structure interactions. This paper concludes with a summary and a prospective view on future trends. This review highlights the robustness and accuracy of the MPM in tackling large deformation problems, offering valuable insights for the analysis of large deformations and damage evolution in various materials.