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On homotopy conditions and the existence of multiple equilibria in finite elasticity

Published online by Cambridge University Press:  14 November 2011

K. D. E. Post  and
J. Sivaloganathan
K. D. E. Post
Affiliation:
Institut für Mathematik–Angewandte Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10 099 Berlin, Germany
J. Sivaloganathan
Affiliation:
School of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K.
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Abstract

In this paper we study homotopy classes of deformations and their properties under weak convergence. As an application, we give an analytic proof (in two and three dimensions) of the existence of infinitely many local minimisers for a displacement boundary-value problem from finite elasticity, posed on a nonconvex domain, under the constitutive assumption of polyconvexity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 3 , 1997 , pp. 595 - 614
Copyright
Copyright © Royal Society of Edinburgh 1997

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