A field theory approach to stability of radial equilibria in nonlinear elasticity

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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 languageEnglish
Pages (from-to)589-604
Number of pages16
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume99
Issue number3
DOIs
Publication statusPublished - May 1986

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ASJC Scopus subject areas

  • Mathematics(all)

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