On Rayleigh-type surface waves in an initially stressed incompressible elastic solid

Abstract

In this paper, we apply the theory of the superposition of infinitesimal deformations on finite deformations in an initially stressed hyperelastic material to the study of the propagation of surface waves in an initially stressed incompressible half-space subjected to a pure homogeneous deformation. This is based on a theory of initial stress in elastic solids due to Shams et al. (2011, Initial stresses in elastic solids: constitutive laws and acoustoelasticity. Wave Motion, 48, 552–567). The initial stress is not itself associated with a finite-elastic deformation and this contrasts with the situation in which the initial stress is a pre-stress that is accompanied by a finite deformation. A general formulation of the equations governing incremental motions is provided and then specialized to two-dimensional motions in a principal plane of the underlying (homogeneous) deformation with a uniform initial stress that is coaxial with the finite deformation. With this specialization, the combined effect of initial stress and finite deformation on the speed of Rayleigh waves is discussed and illustrated graphically with the main emphasis on the effect of initial stress.