Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

K. D. E. Posta1 and J. Sivaloganathana2

a1 Institut für Mathematik–Angewandte Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10 099 Berlin, Germany

a2 School of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K.

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.

(Received November 14 1995)

(Revised October 02 1996)