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$$\Gamma$$-convergence of energies for nematic elastomers in the small strain limit. (English) Zbl 1272.76028
Summary: We study two variational models recently proposed in the literature [A. DeSimone and L. Teresi, Eur. Phys. J. E 29, 191–204 (2009); P. Cesana and A. DeSimone, Math. Models Methods Appl. Sci. 19, No. 4, 601–630 (2009; Zbl 1165.49014)] to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one $$\Gamma$$-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

##### MSC:
 76A15 Liquid crystals 82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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##### References:
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