Scattering of torsional waves by a circular crack in a transversely isotropic solid

The scattering of torsional shear waves by a circular crack located at the interface of two transversely isotropic solids is studied here. The axis of the material symmetry and the axis of the crack coincide. The incident wave is taken as a torsional shear wave propagating perpendicular to the crack surface. Hankel transform representation of the scattered field is used. After some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials, which fulfill the correct edge condition, and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for isotropic as well as anisotropic materials for both homogeneous and inhomogeneous solids. Results for the isotropic and homogeneous solid compare favorably with those available in the literature.