THE INFLUENCE OF SHEAR STRAIN AND HYDROSTATIC STRESS ON STABILITY ANDELASTIC-WAVES IN A LAYER

The theory of incremental motions superimposed on a large static defor mation of an elastic solid is used to investigate the propagation of i nfinitesimal waves along a layer of material of uniform finite thickne ss. The layer is subject to an underlying simple shear deformation acc ompanied by an arbitrary uniform hydrostatic stress. In respect of a g eneral form of incompressible, isotropic elastic strain-energy functio n, the dispersion equation for infinitesimal waves is obtained for two different sets of incremental boundary conditions on the faces of the layer. When the wave speed vanishes the dispersion equation becomes a bifurcation equation, which identifies configurations in which quasi- static incremental deformations can first appear on a path of simple s hearing and hydrostatic stressing from the natural (undeformed, unstre ssed) configuration of the layer. Explicit bifurcation criteria are ob tained for a general form of strain-energy function and their conseque nces are illustrated by numerical results showing the dependence of bi furcation on certain deformation, stress and layer-thickness parameter s. For a particular class of strain-energy functions, dispersion equat ions are obtained in explicit form for both incremental boundary-value problems. and the dependence of the wave speed on the same parameters is illustrated in detail.