Macroscopic response of nematic elastomers via relaxation of a class of SO(3)-invariant energies

We obtain an explicit formula for the relaxation of the free-energy density for nematic elastomers proposed by BLADON, TERENTJEV & WARNER (Phys. Rev. E 47 (1993), 3838-3840). The proof is based on a characterization of the level sets of the relaxed energy. In particular, the construction uses only laminates within laminates and it identifies those deformations that correspond to simple laminates.