Brittle crack propagation simulation based on the Virtual Element Method and Jk-integral fracture criterion

Abstract

Crack propagation simulation is a challenging topic in computational fracture mechanics, and the main issue is modeling the displacement discontinuity in the existing finite element mesh. The Virtual Element Method (VEM), as an extension of the Finite Element Method (FEM), permits the usage of arbitrarily shaped elements, including non-convex polygons or elements with hanging vertices, and has no distortion sensitivity. These features greatly facilitate VEM in addressing the crack propagation problem. An arbitrary crack propagation path can be achieved during the crack propagation process because the local mesh can be modified by adding or deleting vertices and/or edges, and by splitting one element into two polygons. This study simulates brittle crack propagation by the VEM with an element split strategy. The $J_k$-integral fracture criterion has been employed to determine the crack initiation and predict the crack propagation direction for mixed-mode loading conditions. The $J_k$-integral is computed directly by the path integral rather than by the domain integral, and its conservation has been verified. Some numerical applications have been implemented, including a mode-I crack problem test, a shear test of a single-edge notched plate and two different three-point bending tests. The numerical results show good agreement with the experiments, which verify the validity of the proposed simulation method for crack propagation.