On the stability of cavitating equilibria
1. 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 occ i e R3: |x| < 1} in its reference state. We refer to maps — ^ u: 5 —> ti s of the ball and we seek equilibria by minimising the