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We compute the relaxation of the total energy related to a variational modelfor nematic elastomers, involving a nonlinear elastic mechanical energydepending on the orientation of the molecules of the nematic elastomer, and anematic Oseen--Frank energy in the deformed configuration. The main assumptionsare that the quasiconvexification of the mechanical term is polyconvex and thatthe deformation belongs to an Orlicz-Sobolev space with an integrability justabove the space dimension minus one, and does not present cavitation. Webenefit from the fine properties of orientation-preserving maps satisfying thatregularity requirement proven in \cite{HS} and extend the result of \cite{MCOl}to Orlicz spaces with a suitable growth condition at infinity.

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