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Attainment results for nematic elastomers

Part of: Foundations, constitutive equations, rheology Elastic materials Equilibrium (steady-state) problems

Published online by Cambridge University Press:  08 July 2015

Virginia Agostiniani ,
Gianni Dal Maso  and
Antonio DeSimone
Virginia Agostiniani
Affiliation:
OxPDE – Mathematical Institute, Woodstock Road, Oxford OX2 6GG, UK, ([email protected])
Gianni Dal Maso
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy, ([email protected]; [email protected])
Antonio DeSimone
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy, ([email protected]; [email protected])
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Abstract

We consider a class of non-quasi-convex frame indifferent energy densities that includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem, we provide an explicit minimizer of the energy functional satisfying a non-trivial boundary condition. Other attainment results, both for the nonlinear and the linearised model, are obtained by using the theory of convex integration introduced by Müller and Šverák in the context of crystalline solids.

Keywords

nematic elastomersconvex integrationsolenoidal fields

MSC classification

Primary: 74G65: Energy minimization 74B20: Nonlinear elasticity 74B15: Equations linearized about a deformed state (small deformations superposed on large) 76A15: Liquid crystals
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 669 - 701
Copyright
Copyright © Royal Society of Edinburgh 2015 

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