Mode III crack in a laminated medium

Antiplane deformation of a laminated medium with a semi-infinite crack parallel to the interfaces between the layers is considered. The homogeneous, elastic and isotropic layers of two different types are arranged periodically. This allows the reduction of the initial boundary value problem to the Wiener-Hopf equation by combined application of the Laplace and the discrete Fourier transforms. For the specific case of an exponentially decaying load the solution is obtained in closed form by means of rapidly convergent triple integrals. The simple expressions for the stress intensity factor and the energy release rate are derived. For some limiting cases the solution is found to be consistent with previous results. A parametric study gave an opportunity to examine the accuracy of the known approximate sandwich model of multilayered composites.