Analysis of variational models for nematic liquid crystal elastomers
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Mon, 26/01/2009 13:30 |
Pierluigi Cesana (SISSA, Trieste, Italy) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
| The relaxation of a free-energy functional which describes the order-strain interaction in nematic liquid crystal elastomers is obtained explicitly. We work in the regime of small strains (linearized kinematics). Adopting the uniaxial order tensor theory or Frank model to describe the liquid crystal order, we prove that the minima of the relaxed functional exhibit an effective biaxial microstructure, as in de Gennes tensor model. In particular, this implies that the response of the material is soft even if the order of the system is assumed to be fixed. The relaxed energy density satisfies a solenoidal quasiconvexification formula. | |||