An efficient and locking‐free material point method for three‐dimensional analysis with simplex elements

Abstract The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite element methods), when modelling complex geometries with a range of material models. In this paper we present developments of the standard material point method aimed at realizing these goals. The key contribution provided here is the development of a material point method that avoids volumetric locking (arising from elastic or elasto‐plastic material behavior) while using low‐order tetrahedral finite elements for the background computational mesh, hence allowing unstructured background grids to be used for complex geometries. We also show that these developments can be effectively parallelized to improve computational efficiency.