Propagation of interfacial (Stoneley-type) waves at the joint boundary of two initially-stressed incompressible half-spaces

Abstract

The presence of initial stress in solids changes the material’s response to finite and infinitesimal deformations. This paper presents a study on the effects of initial stress, finite deformation, and material properties on the speed of interfacial waves which are assumed to travel at the joint boundary of two incompressible half-spaces. The theory of infinitesimal deformations superimposed on finite deformations is used along with the theory of invariants. Boundary conditions at the interface result in an explicit secular equation, which is analyzed generally. For each half-space, a prototype strain–energy function is assumed, which is a function of the deformation gradient and initial stress tensors. The effect of different governing parameters is observed on the wave speed and is analyzed theoretically. Graphical illustrations are also presented to elaborate on the theoretical results. It is observed that for admissible values of parameters, a real wave speed exists and is bounded by values depending on the governing parameters. A comparison between Rayleigh and interfacial wave speeds is also made and supported with graphs of dimensionless wave speeds with respect to initial stresses.