Finite amplitude waves in incompressible perfectly elastic materials

Abstract

Propagation of finite amplitude plane shear waves in an incompressible perfectly elastic material is considered. The material occupies the half space, X 2 ⩾ 0, and is initially at rest. A translational motion is imparted to the surface. X 2 = 0, by applying a spatially uniform and time-dependent shear stress on this surface. The subsequent deformation and change of state in the material are calculated. Two special problems are considered in detail. In the first, the material is in a stress-free state and the surface, X 2 = 0, is given a uniform motion for time t > 0. In the second, the unloading problem following the removal of the applied stress is calculated. The loading and unloading processes in the material generally follow a distinctly different pattern. Depending on the nature of the material and the loading programme, the shear waves may or may not coalesce into a transverse shock wave. The influence of materials of different nature on the propagation of shear waves is also discussed.