A Rod Theory for Liquid Crystalline Elastomers

We derive a general constitutive model for nematic liquid crystalline rods. Our approach consists in reducing the three-dimensional strain-energy density of a nematic cylindrical structure to a one-dimensional energy of a nematic rod. The reduced one-dimensional model connects directly the optothermal stimulation to the generation of intrinsic curvature, extension, torsion, and twist, and is applicable to a wide range of liquid crystalline rods subject to external stimuli and mechanical loads. For illustration, we obtain the shape of a clamped rod under uniform illumination, and compute the instability of an illuminated rod under tensile load. This general framework can be used to determine the shape and instabilities of nematic rods with different cross-sections or different alignment of the nematic field.