Compound material point method (CMPM) to improve stress recovery for quasi-static problems

Abstract

Stress oscillations and inaccuracies are commonly reported in the material point method (MPM). This paper investigates the causes and presents a method to reduce them. The oscillations are shown to result from, at least in part, two distinctly different causes, both originating from the shape function approximations used. The first is due to the components of the stiffness matrix (or other matrices) being derived by performing numerical integration using the material points, and the second is due to calculating the strain from the nodal displacements of the elements, interpolated to the material points, via the shape function spatial derivatives. In this paper, an improvement for the recovery of results from the nodes to the material points is presented, where an increase of the Cn continuity along with an interpolation involving nodes from neighbouring elements is applied.