Abstract It has been 25 years since Sulsky and her coworkers developed the first version of the material point method (MPM): a quasi particle method to solve continuum mechanics problems. In the MPM, the continua are discretized by Lagrangian particles moving over a fixed Eulerian background grid. As a result, large deformation and contact can be treated effortlessly. Since then, many improved instances of the MPM have been developed and the MPM has found applications in many fields from geoengineering to movie industry. As the MPM has now been matured and a large body of literature on it exists, it is a good time to ponder and reflect on the developments of the method to date. To this end, this manuscript provides a concise introduction to the MPM, covering theory, implementation, and applications. All the algorithms required to have a working MPM implementation for the simulations of solids, fluids, and their interactions are provided. We have coded these algorithms in in-house open source programs and used them to study the performance of different MPM variants for large deformation solid mechanics problems. These problems exhibit large plastic deformation, fractures and contacts. Convergence of different MPMs (CPDI, GIMP, B-splines, total Lagrangian MPM, improved MPMs) are studied. Furthermore, MPM formulations for fluids/gases and heat conduction are also covered. Potential areas for improvement on the method have been identified. The paper is the first review of the MPM and presents a state of the art of the current MPM literature covering 339 references.

Alban de Vaucorbeil

Vinh Phu Nguyen

Sina Sinaie

Jian Ying Wu

Advances in Applied Mechanics

应用力学进展汇集了应用力学所有领域的最新重大进展。自 1948 年出版以来，它旨在提供有关机械科学主题的最高质量、权威的评论文章。它是在力学各个分支领域工作的科学家和工程师的主要兴趣所在，对于那些将力学研究结果应用于航空航天、化学、土木、环境、机械和核工程等领域的人来说也很有价值。

Advances in Applied Mechanics brings together the latest significant developments in all areas of applied mechanics. Since its inception in 1948, it has aimed to provide high-quality, authoritative review articles on topics in mechanical science. It serves as a primary interest for scientists and engineers working in various branches of mechanics and is valuable for those applying the results of mechanics research in fields such as aerospace, chemical, civil, environmental, mechanical, and nuclear engineering.

《Advances in Applied Mechanics》汇集了应用力学各领域的最新重大进展。自1948年创刊以来，该期刊旨在提供机械科学主题的高质量、权威的评论文章。它是力学各个分支领域科学家和工程师的主要关注点，对于那些将力学研究成果应用于航空航天、化学、土木、环境、机械和核工程等领域的研究者来说，具有重要的参考价值。

Category	Quartile
工程技术	1
工程技术, 工程机械	1
工程技术, 力学	1

Material point method after 25 years: Theory, implementation, and applications

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