Representation of singular fields without asymptotic enrichment in the extended finite element method

TL;DR

This paper introduces xSBFEM, a novel extension of XFEM that replaces asymptotic crack tip enrichments with semi-analytical solutions, simplifying computations and improving accuracy in modeling cracks in various materials.

Contribution

It proposes the extended scaled boundary finite element method (xSBFEM), eliminating the need for special numerical integration in XFEM and enhancing crack modeling capabilities.

Findings

Accurate results in benchmark fracture mechanics problems

Improved condition number of the stiffness matrix

Simplified implementation with MATLAB code

Abstract

In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does not require special numerical integration technique to compute the stiffness matrix and it improves the capability of the XFEM to model cracks in homogeneous and/or heterogeneous materials without a priori knowledge of the asymptotic solutions. A heaviside enrichment is used to represent the jump across the discontinuity surface. We call the method as the extended scaled boundary finite element method (xSBFEM). Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics show that the proposed method yields accurate results with improved condition number. A simple MATLAB code is annexed to compute the terms in the stiffness matrix, which can easily be integrated in any existing FEM/XFEM code.