Fracture mechanics analysis of bimaterial interface cracks using the generalized finite difference method

Abstract

This paper makes the first attempt to apply the generalized finite difference method (GFDM), a recently developed meshless collocation method, for fracture mechanics analysis of dissimilar elastic materials with interfacial cracks. The main idea of the GFDM is to divide the entire computational domain into a set of overlapping small subdomains in which the local Taylor series expansion and moving-least square approximation are employed for generating the local systems of linear equations. Since the method is meshless and no element connectivity is needed, the burdensome remeshing procedures associated with the finite element method (FEM) is avoided. The multi-domain GFDM technique is used to handle the non-homogeneity of the cracked dissimilar materials. The displacement extrapolation method (DEM), which avoids the direct calculation of the oscillatory near-tip displacement and stress fields, is employed to compute the complex stress intensity factors (SIFs) for cracked composite bimaterials. Several representative numerical examples are presented and discussed to demonstrate that the present method is highly accurate and relatively robust for interface crack analysis of composite bimaterials.