Nonlocal model for nematic liquid-crystal elastomers

We have developed a fully nonlocal model to describe the dynamic 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 nonlocal 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 the displacement and the 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 for nematic liquid crystals.