Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers (Q2192703)

Summary: 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 [\textit{D. Henao} and \textit{B. Stroffolini}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 194, Article ID 111513, 21 p. (2020; Zbl 1436.74023)] and extend the result of [\textit{C. Mora-Corral} and \textit{M. Oliva}, ESAIM, Control Optim. Calc. Var. 25, Paper No. 19, 27 p. (2019; Zbl 1437.49029)] to Orlicz spaces with a suitable growth condition at infinity.