An Efficient Particle Subdomain Quadrature Scheme for the Material Point Method

Abstract

The material point method (MPM) has been proved to be an effective numerical method for large deformation problems. However, the MPM suffers from the cell crossing error as that the material particles are used to represent the deformed material and to perform the particle quadrature. In this paper, an efficient subdomain quadrature material point method (sqMPM) is proposed to eliminate the cell crossing error efficiently. The particle domain is approximated to be the line segment, rectangle, and cuboid for the one-, two-, and three-dimensional problems, respectively, which are divided into several different subdomains based on the topological relationship between the particle domain and background grid. A single Gauss quadrature point is placed at the center of each subdomain and used for the information mapping. The material quantities of each Gauss quadrature point are determined by the corresponding material particle and the subdomain volume without the cumbersome reconstruction algorithm. Numerical examples for one-, two-, and three-dimensional large deformation problems demonstrate the effectiveness and highly enhanced convergence and efficiency of the proposed sqMPM.