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

Research output: Contribution to journalArticle

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

Fingerprint

Nonlinear Elasticity
Field Theory
Ball
Radial Solutions
Cavitation
Calculus of variations
Form
Class
Interpretation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

@article{5805918b891e4b418fb0ebc3011a8b98,
title = "A field theory approach to stability of radial equilibria in nonlinear elasticity",
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.",
author = "J. Sivaloganathan",
year = "1986",
month = "5",
doi = "10.1017/S0305004100064513",
language = "English",
volume = "99",
pages = "589--604",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "3",

}

TY - JOUR

T1 - A field theory approach to stability of radial equilibria in nonlinear elasticity

AU - Sivaloganathan, J.

PY - 1986/5

Y1 - 1986/5

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84974399477&partnerID=8YFLogxK

U2 - 10.1017/S0305004100064513

DO - 10.1017/S0305004100064513

M3 - Article

VL - 99

SP - 589

EP - 604

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -