Fracture analysis of functionally graded materials by a BEM

In this paper, crack analysis in two-dimensional (2D), continuously nonhomogeneous, isotropic and linear elastic functionally graded materials (FGMs) is presented. For this purpose, a boundary element method (BEM) based on a boundary-domain integral equation formulation is developed. An exponential variation with spatial variables is assumed for Young’s modulus of the FGMs, while a constant Poisson’s ratio is considered. Fundamental solutions for homogeneous, isotropic and linear elastic solids are applied in the formulation. To avoid displacement gradients in the domain integral, normalized displacements are introduced. By using the radial integration method, the domain integral is transformed into boundary integrals over the global boundary. The normalized displacements in the domain integral are approximated by a combination of radial basis functions and polynomials in terms of global coordinates, which leads to a meshless scheme. Special attention of the analysis is devoted to the computation of the most important crack-tip characterizing parameters of cracked FGMs, namely the stress intensity factors. To show the effects of the material gradation on the stress intensity factors, numerical examples are presented and discussed.