A displacement-based and explicit non-planar 3D crack propagation model in the generalized/extended finite element method

Abstract

The displacement-based methods for the extraction of the Stress Intensity Factors (SIFs) were created decades ago and, since them, they have been used in a wide range of numerical analysis, most of them based on standard 2D Finite Element Method (FEM). Although the accuracy of the SIFs computed by the displacement-based methods generally be inferior compared with the energy release methods, the use of the former methods have been motivated by its simplicity, ease of implementation and low computational cost, even though it may yield less accurate SIFs when compared with the latter methods. A major use of the SIFs is the prediction of the crack path direction in crack propagation analysis. The modelling of crack propagation is the most frequent application of the Generalized Finite Element Method (GFEM) and Extended Finite Element Method (XFEM) and a large number of crack propagation models presented in literature uses energy release methods for SIFs evaluation. Very few works using displacement-based methods for the computation of the SIFs have been published in literature in the context of the GFEM and XFEM. This paper presents a propagation model for an explicit non-planar 3D crack in a GFEM/XFEM background. The proposed model uses the Displacement Correlation Method (DCM) for the SIFs extraction. Some crack propagation problems are investigated and the resultant crack paths are compared with reported results from literature. This work demonstrates that the model here proposed generates very reasonable crack paths even for relatively coarse meshes using linear elements.