An integral equation formulation of anti-plane inhomogeneities

In this paper, a boundary integral equation formulation for anti-plane shear inhomogeneous medium is presented to study the interaction between the inhomogeneities and cracks. The proposed boundary integral equation formulation only contains out-of-plane interface displacements and out-of-plane discontinuous displacements over cracks. Numerical implementation is simple since the present formulation has considered the shear equilibrium condition over the interfaces between the matrix and inhomogeneities. Out-of-plane interface displacements and out-of-plane traction integral equations are collocated respectively on the matrix-inhomogeneity interfaces and on one side of the crack surface. Numerical examples are given to show the validity and numerical accuracy of the present method.