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The stability of a Bell-constrained half-space in compression is studied. Tothis end, the propagation of Rayleigh waves on the surface of the material whenit is maintained in a static state of triaxial prestrain is considered. Theprestrain is such that the free surface of the half-space is a principal planeof deformation. The exact secular equation is established for surface wavestraveling in a principal direction of strain with attenuation along theprincipal direction normal to the free plane. As the half-space is put underincreasing compressive loads, the speed of the wave eventually tends to zeroand the bifurcation criterion, or stability equation, is reached.  Then the analysis is specialized to specific forms of strain energy functionsand prestrain, and comparisons are made with results previously obtained in thecase of incompressible neo-Hookean or Mooney-Rivlin materials. It is found thatthese rubber-like incompressible materials may be compressed more than "Bellempirical model" materials, but not as much as "Bell simple hyperelastic"materials, before the critical stretches, solutions to the bifurcationcriterion, are reached. In passing, some classes of incompressible materialswhich possess a relative-universal bifurcation criterion are presented.

Rayleigh waves and surface stability for Bell materials in compression; comparison with rubber