Non-principal surface waves in deformed incompressible materials

TL;DR

This paper develops a method to analyze surface wave propagation in deformed isotropic materials, providing explicit secular equations and numerical examples, including for Mooney-Rivlin materials, without restrictions on strain energy functions.

Contribution

It introduces a generalized approach using the Stroh formalism and Taziev's technique to derive explicit secular equations for surface waves in deformed materials, applicable to a broad class including Mooney-Rivlin.

Findings

Explicit secular equations derived for surface wave speed.

Method applicable to a wide class of strain energy functions.

Numerical examples demonstrate the approach's effectiveness.

Abstract

The Stroh formalism is applied to the analysis of infinitesimal surface wave propagation in a statically, finitely and homogeneously deformed isotropic half-space. The free surface is assumed to coincide with one of the principal planes of the primary strain, but a propagating surface wave is not restricted to a principal direction. A variant of Taziev's technique [Sov. Phys. Acoust. 35 (1989) 535] is used to obtain an explicit expression of the secular equation for the surface wave speed, which possesses no restrictions on the form of the strain energy function. Albeit powerful, this method does not produce a unique solution and additional checks are necessary. However, a class of materials is presented for which an exact secular equation for the surface wave speed can be formulated. This class includes the well-known Mooney-Rivlin model. The main results are illustrated with several numerical examples.