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

J. Sivaloganathan

doi:10.1017/S0305004100064513

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

J. Sivaloganathan

University of East Anglia

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	589-604
Number of pages	16
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	99
Issue number	3
DOIs	https://doi.org/10.1017/S0305004100064513
Publication status	Published - May 1986

ASJC Scopus subject areas

General Mathematics

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AB - 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.

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

Abstract

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