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The propagation of infinitesimal surface waves on a half-space of incompressible isotropic elastic material subject to a general pure homogeneous pre-strain is considered. The secular equation for propagation along a principal axis of the pre-strain is obtained for a general strain-energy function, and conditions which ensure stability of the underlying pre-strain are derived. The influence of the pre-stress on the existence of surface waves is examined and, in particular, it is found that, under a certain range of hydrostatic pre-stress, a unique wavespeed exists and is bounded above by a limiting speed which corresponds to the shear wave speed in an infinite body. The secular equation is analysed in detail for particular deformations and, for a number of specific forms of strain-energy function, numerical results are used to illustrate the dependence of the wave speed on the pre-strain. Particular attention is focused on pre-strains corresponding to loss of stability, in which case the infinitesimal strain is time-independent (the wave speed being zero). The theory described here encompasses previous work on surface waves and instabilities in incompressible isotropic elastic materials and provides a clear delimitation of the range of deformations for which surface waves exist.
Dowaikh et al. (Mon,) studied this question.