Modeling the Dynamics of Shape Change in Liquid Crystal Elastomers

Because of the strong coupling between orientational order and mechanical strain, liquid crystal elastomers can exhibit large and fast responses to external stimuli. The system dynamics can be characterized in terms of the motion of the conserved cross-links and the evolution of the non-conserved orientational order parameter. We have developed a fully non-local free energy for nematic elastomers, and a corresponding dissipation function. Using a Lagrangian formalism, we have obtained from these the equations of motion. We discuss these dynamical equations, the associated boundary conditions, and approaches to providing a numerical solution. We present the current status of our numerical results, and compare these with the results of experiments.