Surface Instability of Rubber in Compression

The previously derived expressions for the incremental elastic coefficients of an isotropic medium under initial stress are applied to rubbertype elasticity. As a corollary an exact theory is obtained for the surface instability of such material under compression. It is found that in plane strain the incremental properties remain isotropic and are characterized by a single strain-dependent modulus. In three-dimensional strain the elastic properties are found to coincide with those of the elastic medium introduced by Green to illustrate the properties of electromagnetic propagation. The apparent rigidity of the surface as a function of strain is evaluated and is shown to result from the combined effect of the variation of rigidity modulus and a membrane effect due to the initial stress. At a critical compression the two effects act in opposite directions and the apparent surface rigidity vanishes causing incipient instability. The phenomenon is formally analogous to Rayleigh waves. Attention is also called to the existence of interfacial instability at a surface of discontinuity of two elastic media under initial stress in analogy with Stoneley waves.