Calculus of Variations and Geometric Measure Theory
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G. Scilla - B. Stroffolini

Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers

created by scilla on 12 Jun 2019
modified on 21 Nov 2019


Accepted Paper

Inserted: 12 jun 2019
Last Updated: 21 nov 2019

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Year: 2019


We compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic Oseen-Frank energy in the deformed con guration. The main assumptions are that the quasiconvexi cation of the mechanical term is polyconvex and that the deformation belongs to an Orlicz-Sobolev space with an integrability just above the space dimension minus one, and does not present cavitation. We benefi t from the fine properties of orientation-preserving maps satisfying that regularity requirement proven in Stroffolini-Henao and extend the result of Mora Corral-Oliva to Orlicz spaces with a suitable growth condition at in finity.

Keywords: relaxation, nonlinear elasticity, nematic elastomers, Orlicz-Sobolev spaces, orientation-preserving maps


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