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Existence theorem for nonlinear micropolar elasticity

Published online by Cambridge University Press:  21 October 2008

Josip Tambača  and
Igor Velčić
Josip Tambača
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia. tambaca@math.hr; ivelcic@math.hr
Igor Velčić
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia. tambaca@math.hr; ivelcic@math.hr
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Abstract

In this paper we give an existence theorem for the equilibrium problem for nonlinear micropolar elastic body. We consider the problem in its minimization formulation and apply the direct methods of the calculus of variations. As the main step towards the existence theorem, under some conditions, we prove the equivalence of the sequential weak lower semicontinuity of the total energy and the quasiconvexity, in some variables, of the stored energy function.

Keywords

Micropolar elasticityexistence theoremquasiconvexity
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 92 - 110
Copyright
© EDP Sciences, SMAI, 2008

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