Extended isogeometric analysis of cracks in a plate

Abstract

An Extended Isogeometric Analysis (XIGA) formulation has been implemented on MATLAB platform to compute mixed-mode stress intensity factors (SIFs) and displacements for cracks in homogenous material and bimaterial plate, specifically for center and edge crack samples and simulate single crack propagation in homogenous material with voids and inclusions. The proposed method confirms numerically that it outperforms the Extended Finite Element Method (XFEM) in accuracy and computational efficiency. NURBS (non-uniform rational B-splines) based XIGA does not require remeshing thus reducing significant computation time has already been applied to material modelling as well as discrete and diffuse modelling of crack propagation which allow efficient local refinement while maintaining higher-order continuity and exact geometry. The crack faces are modelled by the discontinuous Heaviside function. The stress singularity of the crack tip is modelled by the enrichment function. The voids and inclusions are modelled by the Heaviside function and the distance function. The interaction integral for homogeneous materials is used to compute the SIFs of the crack tip. The improved performance of the method is confirmed by numerical examples and compared with those of other methods available in the literature.