Non-principal Rayleigh waves in deformed transversely isotropic incompressible non-linearly elastic solids

An explicit expression of the secular equation for non-principal Rayleigh waves in incompressible, transversely isotropic, pre-stressed elastic half-spaces is obtained. This generalizes previous works dealing with isotropic incompressible materials. The free surface coincides with one of the principal planes of the primary pure homogeneous strain, but the surface wave is not restricted to propagate in a principal direction. The free surface is taken to be the horizontal plane, while the fibres that give the transversely isotropic character of the material are located throughout the whole half-space and run parallel to each other and perpendicular to the depth direction. Results are given, for illustration, in respect of the so-called reinforcing models. It is shown that the wave velocity depends strongly on the anisotropic character of the material model.