A Virtual Element Method for 2D linear elastic fracture analysis

TL;DR

This paper introduces a Virtual Element Method (VEM) for 2D linear elastic fracture analysis, emphasizing mesh flexibility, adaptive refinement, and accurate stress intensity factor computation, validated through convergence studies and crack growth prediction.

Contribution

It develops a novel VEM approach for fracture mechanics that handles arbitrary polygonal meshes and includes adaptive refinement strategies for crack propagation analysis.

Findings

VEM achieves convergence rates comparable to FEM.

Adaptive mesh refinement improves crack growth prediction.

VEM effectively handles arbitrary polygonal meshes with hanging nodes.

Abstract

This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an adaptive mesh refinement strategy based on the superconvergent patch recovery for triangular, quadrilateral as well as for arbitrary polygonal meshes. For the local stiffness matrix in VEM, we adopt a stabilization term which is stable for both isotropic scaling and ratio. Stress intensity factors (SIFs) of a polygonal mesh are discussed and solved by using the interaction domain integral. The present VEM formulations are finally tested and validated by studying its convergence rate for both continuous and discontinuous problems, and are compared with the optimal convergence rate in the conventional Finite Element Method (FEM). Furthermore, the adaptive mesh refinement strategies used to effectively predict the crack growth with the existence of hanging nodes in nonconforming elements are examined.