Large-amplitude Love waves

Abstract

In the context of the finite elasticity theory, we consider a model for compressible solids called 'compressible neo-Hookean material'. We show how finite-amplitude inhomogeneous plane wave solutions and finite-amplitude unattenuated solutions can combine to form a finite-amplitude Love wave. We take a layer of finite thickness overlying a solid half-space, both made of different prestressed compressible neo-Hookean materials. We derive an exact solution of the equations of motion and boundary conditions and also obtain results for the energy density and the energy flux of the waves. Finally, we investigate the special case when the interface between the layer and the substrate is in a principal plane of the prestrain. A numerical example is given.