  An isotropic elastic half space is prestrained so that two of the principal
axes of strain lie in the bounding plane, which itself remains free of
traction. The material is subject to an isotropic constraint of arbitrary
nature. A surface wave is propagated sinusoidally along the bounding surface in
the 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 principal
surface wave; it is cubic in a quantity whose square is linearly related to the
squared wave speed. For the prestrained material, replacing the squared wave
speed by zero gives an explicit bifurcation, or stability, criterion.
Conditions on the existence and uniqueness of surface waves are given. The
bifurcation criterion is derived for specific strain energies in the case of
four isotropic constraints: those of incompressibility, Bell, constant area,
and Ericksen. In each case investigated, the bifurcation criterion is found to
be 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 of
arterial wall mechanics are also presented.
