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An isotropic elastic half space is prestrained so that two of the principalaxes of strain lie in the bounding plane, which itself remains free oftraction. The material is subject to an isotropic constraint of arbitrarynature. A surface wave is propagated sinusoidally along the bounding surface inthe direction of a principal axis of strain and decays away from the surface.The exact secular equation is derived by a direct method for such a principalsurface wave; it is cubic in a quantity whose square is linearly related to thesquared wave speed. For the prestrained material, replacing the squared wavespeed by zero gives an explicit bifurcation, or stability, criterion.Conditions on the existence and uniqueness of surface waves are given. Thebifurcation criterion is derived for specific strain energies in the case offour isotropic constraints: those of incompressibility, Bell, constant area,and Ericksen. In each case investigated, the bifurcation criterion is found tobe of a universal nature in that it depends only on the principal stretches,not on the material constants. Some results related to the surface stability ofarterial wall mechanics are also presented.

Surface waves in a deformed isotropic hyperelastic material subject to an isotropic internal constraint