  The stability of a Bell-constrained half-space in compression is studied. To
this end, the propagation of Rayleigh waves on the surface of the material when
it is maintained in a static state of triaxial prestrain is considered. The
prestrain is such that the free surface of the half-space is a principal plane
of deformation. The exact secular equation is established for surface waves
traveling in a principal direction of strain with attenuation along the
principal direction normal to the free plane. As the half-space is put under
increasing compressive loads, the speed of the wave eventually tends to zero
and the bifurcation criterion, or stability equation, is reached.
  Then the analysis is specialized to specific forms of strain energy functions
and prestrain, and comparisons are made with results previously obtained in the
case of incompressible neo-Hookean or Mooney-Rivlin materials. It is found that
these rubber-like incompressible materials may be compressed more than "Bell
empirical model" materials, but not as much as "Bell simple hyperelastic"
materials, before the critical stretches, solutions to the bifurcation
criterion, are reached. In passing, some classes of incompressible materials
which possess a relative-universal bifurcation criterion are presented.
