The effect of pre-strain on the reflection and transmission of plane waves at an elastic interface

Abstract

This paper illustrates the influence of pure homogeneous strain on the reflection and transmission of plane waves at the boundary between two half-spaces of incompressible isotropic elastic material. In general, the half-spaces consist of different material and are subjected to different deformations but with their principal axes aligned. For a certain class of constitutive laws it is shown that a homogeneous plane (SV) wave incident on the boundary from one half-space gives rise to a reflected wave (with angle of reflection equal to the angle of incidence) together with an interfacial wave in the same half-space, while in the other half-space two possibilities arise depending on the angle of incidence, the material properties and the magnitudes of the deformations in the two half-spaces. Either (a) there is a transmitted (homogeneous plane) wave accompanied by an interfacial wave, or (b) there are two interfacial waves with equal speeds of propagation but different rates of (spatial) decay away from the boundary. For a second class of constitutive laws similar behaviour is found for certain combinations of angle of incidence, material properties and deformations, but additional possibilities also arise. In particular, there may be two reflected waves instead of one reflected wave and an interfacial wave, coupled with either possibility (a) or (b) in the second half-space. Equally, there may be two transmitted waves for each of the possible combinations of reflected and interfacial waves in the first half-space. For each class of materials conditions under which the incident wave is not refracted are identified and the dependence of the amplitudes of the reflected, transmitted and interfacial waves on the angle of incidence, the states of deformation and the materials is illustrated graphically.