  We consider a continuum model describing the dynamic behavior of nematic
liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the
governing equations. In the model, the Helmholtz free energy and Rayleigh
dissipation are used, within a Lagrangian framework, to obtain the equations of
motion. The free energy consists of both elastic and liquid crystalline
contributions, each of which is a function of the material displacement and the
orientational order parameter. The model gives dynamics for the material
displacement, the scalar order parameter and the nematic director, the latter
two of which correspond to the orientational order parameter tensor. Our
simulations are carried out by solving the governing equations using an
implicit-explicit scheme and the Chebyshev polynomial method. The simulations
show that the model can successfully capture the shape changing dynamics of
LCEs that have been observed in experiments, and also track the evolution of
the order parameter tensor.
