Scattering of SH-waves by an elliptic cavity/crack beneath the interface between functionally graded and homogeneous half-spaces via multipole expansion method

In this study, based on multipole expansion method an analytical treatment is presented for the anti-plane scattering of SH-waves by an arbitrarily oriented elliptic cavity/crack which is embedded near the interface between exponentially graded and homogeneous half-spaces. The cavity is embedded within the inhomogeneous half-space. The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy (i) the governing equation in each half-space, (ii) the continuity conditions across the interface between the two half-spaces, and (iii) the far-field radiation and regularity conditions. The analytical expressions for the scattered elastodynamic fields are derived and the dynamic stress concentration factor associated with the elliptic cavity as well as the dynamic stress intensity factor relevant to the case of a crack are calculated. In the given numerical examples, the effects of such parameters as the incident wave number, angle of the incident waves, the distance of the cavity to the bimaterial interface, and the aspect ratio and the orientation of the elliptic cavity/crack on the scattered field are addressed in detail. It is seen that such parameters have significant effect on the dynamic response of the medium.