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; Maso, Gianni Dal; Desimone, Antonio. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 2015, 145:4(2015), pp. 669-701. [10.1017/S0308210515000128]
Attainment results for nematic elastomers
Agostiniani, Virginia;
2015-01-01
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.| File | Dimensione | Formato | |
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