Non-principal surface waves in deformed incompressible materials

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 [R.M. Taziev, Dispersion relation for acoustic waves in an anisotropic elastic half-space, Sov. Phys. Acoust. 35 (1989) 535–538] 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.