Extended virtual element method for two-dimensional linear elastic fracture

TL;DR

This paper introduces an extended virtual element method (X-VEM) for 2D linear elastic fracture, enabling mesh-independent modeling of crack discontinuities and singularities with high accuracy and optimal convergence.

Contribution

The paper develops an extended VEM with enrichment functions for crack modeling, including an efficient scheme for stress intensity factor computation, advancing numerical fracture analysis.

Findings

Demonstrates high accuracy in benchmark fracture problems

Achieves optimal convergence in energy norm

Effectively models mixed-mode crack problems

Abstract

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes. For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis functions by suitable enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The design of the X-VEM requires an extended projector that maps functions lying in the extended virtual element space onto a set spanned by linear polynomials and the enrichment fields. An efficient scheme to compute the mixed-mode stress intensity factors using the domain form of the interaction integral is described. The formulation permits integration of weakly singular functions to be performed over the boundary edges of the element. Numerical experiments are conducted on benchmark mixed-mode linear elastic fracture problems that demonstrate the sound accuracy and optimal convergence in energy of the proposed formulation.