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

This pager illustrates the influence of pure homogeneous strain on the refl ection and transmission of plane waves at the boundary between two half-spa ces of incompressible isotropic elastic material. In general, the half-spac es consist of different material and are subjected to different deformation s but with their principal axes aligned. For a certain class of constitutive laws it is shown that a homogeneous pla ne (SV) wave incident on the boundary from one half-space gives rise to a r eflected wave (with angle of reflection equal to the angle of incidence) to gether 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 accompa nied by an interfacial wave, or (b) there are two interfacial waves with eq ual 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 cert ain combinations of angle of incidence, material properties and deformation s, but additional possibilities also arise. In particular, there may be two reflected waves instead of one reflected wave and an interfacial wave, cou pled 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 refle cted, transmitted and interfacial waves on the angle of incidence, the stat es of deformation and the materials is illustrated graphically. (C) 2001 El sevier Science Ltd. All rights reserved.