Large-amplitude love waves

In the context of the finite elasticity theory, we considera model for compressible solids called ‘compressible neo-Hookeanmaterial’. We show how finite-amplitude inhomogeneousplane wave solutions and finite-amplitude unattenuated solutionscan combine to form a finite-amplitude Love wave. We take alayer of finite thickness overlying a solid half-space, bothmade of different prestressed compressible neo-Hookean materials.We derive an exact solution of the equations of motion and boundaryconditions and also obtain results for the energy density andthe energy flux of the waves. Finally, we investigate the specialcase when the interface between the layer and the substrateis in a principal plane of the prestrain. A numerical exampleis given.