Abstract
In this paper we study the stability of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity, in which a hole forms at the centre of a ball of isotropic material held in a state of tension under prescribed boundary displacements. The existence of such cavitating solutions has been shown by Ball[1], Stuart [11] and Sivaloganathan[10]. Our methods involve elements of the field theory of the calculus of variations and provide a new unified interpretation of the phenomenon of cavitation.
| Original language | English |
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| Pages (from-to) | 589-604 |
| Number of pages | 16 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Volume | 99 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - May 1986 |
Funding
I would like to thank J. M. Ball who first motivated my interest in thefieldtheory by noticing the existence of two fields of extremals. The work contained in this paper was carried out at Heriot-Watt University under a Science and Engineering Research Council Studentship and grant.
ASJC Scopus subject areas
- General Mathematics