An h-adaptive meshfree-enriched finite element method based on convex approximations for the three-dimensional ductile crack propagation simulation

Abstract

A new numerical approach for modeling the three-dimensional ductile crack propagation problem is presented. The approach is obtained by the introduction of an h-adaptive finite element refinement scheme using the element-wise meshfree enrichments and meshfree visibility criteria to achieve the desired accuracy due to the material nonlinearity and topological changes in the presence of displacement discontinuity. To ensure the element compatibility condition, meshfree convex approximations are employed to the finite element refinement scheme. A crack propagation algorithm combining the meshfree discretization and the crack surface tracking scheme is proposed. To further simplify the freeform surface generation in this moving discontinuity problem, a meshfree particle integration method is considered. Finally, two numerical benchmarks are studied to examine the effectiveness of present method in the three-dimensional ductile crack propagation analysis.