Effects of interfacial elasticity on the reflection and refraction of SH waves

Abstract

The stiffnesses and microstructures of interfaces may have significant influence on the propagation of elastic waves. In this paper, we investigate the reflection and refraction of SH waves at a non-ideal interface between two elastic half-spaces. First, we use the surface elasticity theory (Gurtin and Murdoch in Arch. Ration. Mech. Anal. 57: 291–323, 1975) to describe the mechanical behaviour of the interface. We derive the reflection and transmission coefficients, as well as the phase angles of the reflected and transmitted waves. Then we treat the non-ideal interface between two elastic bodies as a thin membrane with microstructures. By employing the second-order strain-gradient model (Aifantis in Int. J. Eng. Sci. 30: 1279–1299, 1992) to describe the mechanical behaviour of the thin membrane, we establish the strain-gradient thin membrane model for the present problem. Finally, by selecting combinations of non-dimensional parameters, we demonstrate the effects of interfacial material constants on the reflection and refraction of SH waves.