Evaluating material point methods on problems involving free surfaces and strong gradients

Abstract

The material point method (MPM) enables large‐deformation simulations of complex material behaviors with natural multi‐material coupling. However, MPM struggles to accurately capture fields related to material discontinuities, for example, traction‐free surfaces, making MPM fracture simulation challenging. Many MPMs seek to alleviate this challenge, but comparing these approaches has been elusive. This work presents a benchmarking process for evaluating and comparing discontinuous MPM approaches. The benchmarks focus field quantities near a circular hole in a plate and a planar crack with comparisons to accurate finite element solutions.