Material instabilities in nematic elastomers
Antonio DeSimone and Georg Dolzmann
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Submission date: 23. Jan. 1999
published in: Physica / D, 136 (2000) 1-2, p. 175-191
DOI number (of the published article): 10.1016/S0167-2789(99)00153-0
Keywords and phrases: elastometric polymers, liquid crystals, calculus of variations, domain structures, phase transitions
Soft deformation paths and domain patterns in nematic elastomers are analyzed through the minimization of a nonconvex free-energy, recently proposed in the literature. The free-energy density has multiple wells, and is not restricted to small deformations. The problems of calculating the quasiconvex hull of the energy wells and the quasiconvex envelope of the free-energy density are formulated and solved (the latter only in two spatial dimensions). This leads to a complete characterization of the set of soft deformation paths available to a given material, and of its effective macroscopic energy.