Integral identities for fracture along imperfectly joined anisotropic ceramic bimaterials

We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and displacements for both the in-plane and out-of-plane fields. The problem can be considered as modelling bimaterial ceramics which are joined with a thin soft adhesive substance. The integral equations for the out-of-plane problem are solved numerically for orthotropic bimaterials with differing orientations of anisotropy and for different extents of interfacial imperfection. These results are then compared with finite element computations.