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Boundary integral formulation for cracks at imperfect interfaces

We consider an infinite bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The crack is loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity, we derive the corresponding boundary integral formulation, relating physical quantities. The boundary integral equations derived in this paper in the imperfect interface setting show a weak singularity, in contrast to the perfect interface case, where the kernel is of the Cauchy type. We further present three alternative variants of the boundary integral equations which offer computationally favourable alternatives for certain sets of parameters.