Anisotropic bodies with inhomogeneities: The case of a set of cracks

We use the Betti theorem to obtain the integral equations of the dynamic theory of elasticity for a multilayer convex body with an arbitrary elastic anisotropy of layers containing plane infinitely thin cracks. The systems of integral equations relate the displacement jumps to the stresses on the crack lips and are stated numerically in terms of Fourier transforms. For the case of plane-parallel layers with a set of plane cracks on the interfaces between the layers, we propose a simple numerical-analytic method for constructing the Fourier symbol, i.e., the matrix of the kernel of the system of integral equations. The method is stable for an arbitrary combination of continuous and discontinuous conditions on the layer boundaries. Numerical examples are given for a packet of four heterogeneous anisotropic layers.