On the stability of cavitating equilibria
Jeyabal Sivaloganathan · Quarterly of Applied Mathematics · 1995
On the stability of cavitating equilibria.The mathematical phenomenon of cavitation in the setting of finite elasticity was first demonstrated by Ball in [3].This work was subsequently extended and generalised in [23,21,15] and many aspects of the problem are now well understood (see [1,9,10,11,12,15,17,22,18,8] and the references therein).It is known that these cavitating equilibria, which correspond to discontinuous radial deformations of a ball of hyperelastic material, are often global minimisers of the stored energy in classes of radial maps of the ball (see [3,21,22]).In this paper we demonstrate certain stability properties of these cavitating equilibria 1 P with respect to general (not necessarily radial) variations in W ' (B).The setting for this work is a ball of compressible isotropic hyperelastic material xupying the region B = {x B -» R3 as deformations corresponding stored energy occupying the region B = {x e R3: |x| R as deformations of the ball and we seek equilibria by minimising the