On interface waves in misoriented pre-stressed incompressible elastic solids

TL;DR

This paper develops explicit equations for interface waves in misoriented, pre-stressed incompressible elastic solids, simplifying analysis of wave propagation and stability without using the Stroh formalism.

Contribution

It introduces fundamental relationships and explicit secular equations for interface wave problems in anisotropic elastic half-spaces with misaligned principal axes.

Findings

Derived explicit secular equations for interface waves.

Analyzed Stoneley wave propagation in misoriented pre-stressed materials.

Investigated interface stability under complex boundary conditions.

Abstract

Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of anisotropic elastic half-spaces, such as Rayleigh, Sholte, or Stoneley waves. They are obtained rapidly, without recourse to the Stroh formalism. As an application, the problems of Stoneley wave propagation and of interface stability for misaligned predeformed incompressible half-spaces are treated. The upper and lower half-spaces are made of the same material, subject to the same prestress, and are rigidly bonded along a common principal plane. The principal axes in this plane do not however coincide, and the wave propagation is studied in the direction of the bisectrix of the angle between a principal axis of the upper half-space and a principal axis of the lower half-space.