Interface waves in pre-stressed incompressible solids

Abstract

We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semi-infinite solid. With a view to model loaded elastomers and soft tissues, we focus on incompressible solids, subjected to large homogeneous static deformations. The resulting strain-induced anisotropy complicates matters for the incremental boundary value problem, but we transpose and take advantage of powerful techniques and results from the linear anisotropic elastodynamics theory. In particular we cover several situations where fully explicit secular equations can be derived, including Rayleigh and Stoneley waves in principal directions, and Rayleigh waves polarized in a principal plane or propagating in any direction in a principal plane. We also discuss the merits of polynomial secular equations with respect to more robust, but less transparent, exact secular equations.