Macroscopic response of nematic elastomers via relaxation of a class of SO(3)-invariant energies
Antonio DeSimone and Georg Dolzmann
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Submission date: 12. Jul. 2001
published in: Archive for rational mechanics and analysis, 161 (2002) 3, p. 181-204
DOI number (of the published article): 10.1007/s002050100174
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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.