Stability of radially symmetric deformations of spheres of compressible non-linearly elastic materials

Abstract

The stability of homogeneous, isotropic, compressible pressurized non-linearly elastic spheres is considered. A simplified form of the classical method of adjacent equilibria is employed, where the assumed perturbed solution depends only on the radial co-ordinate of the undeformed configuration. The differential equation describing such perturbations and the associated boundary conditions are obtained for all compressible materials and an explicit instability criterion is then obtained. This criterion is studied for three general isotropic materials. The most general form of the strain-energy function for each of the corresponding three radially symmetric deformations is obtained. It is shown that the instability criterion also corresponds to the turning points of the corresponding pressure-inflation relation.