Surface waves in a stretched and sheared incompressible elastic material

TL;DR

This paper investigates how combined homogeneous strain and simple shear affect surface wave propagation in incompressible elastic materials, providing explicit secular equations for special cases and numerical analysis for specific material models.

Contribution

It extends previous work by analyzing combined strain and shear effects on surface waves and derives explicit secular equations for certain material classes.

Findings

Surface wave speed depends on strain and shear levels.

Explicit secular equations are obtained for special material models.

Numerical results illustrate the influence of strain and shear on wave propagation.

Abstract

In this paper we analyze the effect of a combined pure homogeneous strain and simple shear in a principal plane of the latter on the propagation of surface waves for an incompressible isotropic elastic half-space whose boundary is normal to the glide planes of the shear. This generalizes previous work in which, separately, pure homogeneous strain and simple shear were considered. For a special class of materials the secular equation is obtained in explicit form and then specialized to recover results obtained previously for the two cases mentioned above. A method for obtaining the secular equation for a general form of strain-energy function is then outlined. In general this is very lengthy and the result is not listed, but, for the case in which there is no normal stress on the half-space boundary, the result is given, for illustration, in respect of the so-called generalized Varga material. Numerical results are given to show how the surface wave speed depends on both the underlying pure homogeneous strain and the superimposed simple shear. Further numerical results are provided for the Gent model of limiting chain extensibility.