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.