Effect of initial stress on Love wave propagation at the boundary between a layer and a half-space

• Uses general theory of initial stress in nonlinear elasticity.
• Illustrates the effect of initial stress on the speed of Love waves.
• For tensile initial stress, wave speed increases with increasing wave number.
• For compressional initial stress, wave speed decreases with increasing wave number.

In this paper, a discussion on the effects of initial stress and finite deformation on the speed of Love waves propagating along the boundary between a half-space and a layer is carried out. Here, both the half-space and the layer are assumed to be incompressible and initially stressed in their reference configuration. The initial stress in this problem is not associated with a finite elastic deformation which is in contrast to the situation where 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 the specialized case of in-plane motions is considered. The theory of superposition of infinitesimal deformations on finite deformations is applied for initially-stressed incompressible materials. The principal plane of the underlying (homogeneous) deformation with a uniform initial stress is assumed to be coaxial with the finite deformation. With this specialization, the combined effect of initial stress and finite deformation on the speed of Love waves is discussed and the results are analyzed graphically with the main emphasis on the effect of initial stress on wave speed.