Material point method and its applications

Material point method (MPM) discretizes the material domain by particles, and solves the momentum equations on a predefined background mesh. MPM avoids mesh entanglement and involving convection term, by taking advantages of both the Lagrangian and the Eulerian methods. So it is very promising in the numerical simulation of problems involving extreme material deformation and fracture. The state of the art of the theory, the algorithm development and implementation, and the software development of material point method are reviewed in detail. The generalized material point method, the contact algorithm, the adaptive algorithm, the parallel algorithm, and the coupling with other methods are included. Applications of MPM to the problems involving extreme material deformation, such as hypervelocity impact, penetration, explosion, dynamic fracture, fluid-structure interaction, multiscale analysis, and granular material flow and rock and soil failure, are investigated systematically. The applications demonstrate the advantages of MPM over conventional numerical methods.