Dynamic anti-plane response of circular inclusion in bi-material structure with interfacial periodic cracks due to the SH wave

Abstract

This paper investigates the dynamic anti-plane response of the circular inclusion in the bi-material structure with interfacial periodic cracks due to the SH wave. In our analysis, we use the ‘conjunction’ technology and Green’s function method. The bi-material structure consists of two isotropic elastic right-angle domains consisting of a circular elastic inclusion and a series of periodic cracks at the bi-material interface. The periodic cracks are created to satisfy the free conditions of the stresses by using the interface ‘conjunction’ technology. The Green’s functions are also solved to obtain the displacement solutions of the out-place point source loaded on the vertical boundaries of the right-angle plane. The first Fredholm integral equations with unknown force systems are then established based on the continuity conditions at the bi-material interface. As an example, the distributions of the dynamic stress concentration factor (DSCF) around the circular inclusion are obtained and shown graphically. The numerical results indicate that compared with a single crack having periodic cracks strengthens the situation of the dynamic stress concentration around the inclusion.