Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

Abstract

A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.