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.

Attainment results for nematic elastomers

Agostiniani, Virginia;Dal Maso, Gianni;De Simone, Antonio
2015

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.
2015
Settore ICAR/08 - Scienza delle Costruzioni
nematic elastomers; convex integration; solenoidal fields
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/83944
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