Integral identities for an interfacial crack in an anisotropic   bimaterial with an imperfect interface
  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 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. 
Lewis Pryce, Adam Vellender and Alexander Zagnetko
math-ph math.MP