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A Non-Local Model for Liquid Crystal Elastomers

Peter Palffy-Muhoray ,Roland Ennis ,Luis Malacarne ²,Michael Shelley ³
Lliquid Crystal Institute, Kent State University Liquid Crystal Institute, Kent State University ²Dept. of Physics, University of Maringa ³Courant Institute, New York University
We have developed a fully non-local model to describe the behavior of nematic liquid crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through non-local interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion, for displacement and orientational order, are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of long wavelength and small amplitude variations of displacement and orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory.

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