  Liquid crystal elastomers represent a novel class of programmable
shape-transforming materials whose shape change trajectory is encoded in the
material's nematic director field. Using three-dimensional nonlinear finite
element elastodynamics simulation, we model a variety of different actuation
geometries and device designs: thin films containing topological defects,
patterns that induce formation of folds and twists, and a bas-relief structure.
The inclusion of finite bending energy in the simulation model reveals features
of actuation trajectory that may be absent when bending energy is neglected. We
examine geometries with a director pattern uniform through the film thickness
encoding multiple regions of positive Gaussian curvature. Simulations indicate
that heating such a system uniformly produces a disordered state with curved
regions emerging randomly in both directions due to the film's up-down
symmetry. By contrast, applying a thermal gradient by heating the material
first on one side breaks up-down symmetry and results in a deterministic
trajectory producing a more ordered final shape. We demonstrate that a folding
zone design containing cut-out areas accommodates transverse displacements
without warping or buckling; and demonstrate that bas-relief and more complex
bent-twisted structures can be assembled by combining simple design motifs.
