Macroscopic Response of¶Nematic Elastomers via Relaxation of¶a Class of SO(3)-Invariant Energies

Abstract

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.