Mon, 26 Jan 2009
13:30 -
14:30
Gibson 1st Floor SR
Analysis of variational models for nematic liquid crystal elastomers
Pierluigi Cesana
(SISSA, Trieste, Italy)
Abstract
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.