Boundary element analysis of infinite anisotropic elastic medium containing inclusions and cracks

The purpose of this paper is to investigate the interaction between inclusions and cracks in an infinite anisotropic elastic medium (matrix) subject to a remote loading using the boundary element method. The displacement boundary integral equation is used for the matrix and the inclusion, respectively, when the source points are located on the inclusion-matrix interfaces, whilst the stress boundary integral equation is enforced only for the matrix when the source points are acting on the crack surfaces. Quadratic continuous isoparametric boundary elements are employed to discretize the inclusion-matrix interfaces, whilst quadratic discontinuous boundary elements are used to model the crack surfaces. Special crack tip elements are adopted to model the r variation of displacements near the crack tips. The inclusion-matrix interfaces are assumed to be perfectly bonded. Based on this assumption, the resulting system of equations can be formed to obtain the interface unknowns, i.e. displacements and tractions, and the discontinuous displacements over the crack surfaces. Thus, the stress intensity factors at the crack tips can be obtained from the discontinuous displacements at the crack tip elements based on one point displacement formulation. Some examples are given to show accuracy and effectiveness of the boundary element method.