Analysis of three‐dimensional crack initiation and propagation using the extended finite element method

TLDR

The authors introduce a new formulation and numerical procedure for quasi‑static 3‑D crack propagation analysis in brittle and quasi‑brittle solids. They employ the extended finite element method with linear tetrahedral elements, coupled to a viscosity‑regularized continuum damage model to create a crack‑band XFEM, discretizing the evolving discontinuity surface with C0 triangles and quadrilaterals, and enabling closed‑form integration for efficient large‑scale 3‑D simulations. Illustrative examples demonstrate that the method yields accurate crack propagation results. An erratum was published for this article (Int.

Abstract

Abstract An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2005, 63(8): 1228. We present a new formulation and a numerical procedure for the quasi‐static analysis of three‐dimensional crack propagation in brittle and quasi‐brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity‐regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized ‘crack‐band’ version of XFEM. The evolving discontinuity surface is discretized through a C 0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing large‐scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved. Copyright © 2005 John Wiley & Sons, Ltd.