Interface waves in pre-stressed incompressible solids

TL;DR

This paper investigates interface wave propagation in pre-stressed incompressible solids, deriving explicit secular equations for various wave types and directions, with applications to elastomers and soft tissues.

Contribution

It extends incremental wave analysis to incompressible, pre-stressed solids, providing explicit secular equations for different wave modes and propagation directions.

Findings

Explicit secular equations for Rayleigh and Stoneley waves

Analysis of wave polarization and propagation directions

Comparison of polynomial and exact secular equations

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.