We model the dynamics of shape evolution of liquid crystal elastomers (LCE) in three dimensions using finite element
elastodynamics. The model predicts the macroscopic mechanical response induced by changes in nematic order, e.g. by
heating or cooling through the isotropic/nematic transition or, in azo-doped materials, by exposure to light. We model
the performance of LCE actuator devices including multicomponent actuators, peristaltic pumps and self-propelled
robots. The goal of this work is to build a bridge between basic soft matter theory and practical materials
engineering/device design. Supported by NSF-DMR-0605889.