Calculus of Variations and Geometric Measure Theory

G. Scilla - B. Stroffolini

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

created by scilla on 12 Jun 2019
modified on 30 Jun 2020


Published Paper

Inserted: 12 jun 2019
Last Updated: 30 jun 2020

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Volume: 31
Number: 2
Pages: 349-389
Year: 2020
Doi: 10.4171/RLM/895

ArXiv: 1906.05713 PDF


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 configuration. The main assumptions are that the quasiconvexification 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 benefit 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 infinity.

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