Extended material point method for the three‐dimensional crack problems

Abstract

AbstractThe material point method (MPM) has demonstrated itself as an effective numerical method to simulate extreme events with large deformations including fracture problems. However, the traditional MPM encounters difficulties in simulating discontinuities due to its continuous nodal shape function. In this paper, The eXtended Material Point Method (XMPM) is proposed to simulate the three‐dimensional (3D) crack propagation. The XMPM modifies the particle displacement approximation by introducing the local enrichment functions based on the partition of unity into the MPM framework. To accurately trace the evolution of the crack surface, the XMPM employs both the level set method and an extra set of crack surface mesh, which is independent of the background grid. Only locally enriching the nodes near the crack makes the XMPM efficient and able to multiple cracks without extra tricks. Besides, a series of adaptive crack front processing methods, including crack front splitting, merging and locking with its meeting the material boundary, are developed in the XMPM framework to ensure the continuity and smoothness of the crack surface. Numerical examples demonstrate the capability of XMPM to simulate the discontinuity, calculate the fracture parameters and handle the evolution of the crack surface growth in 3D dynamic crack propagation.