Wrinkling in thin nematic elastomers

Coupling a nematic liquid crystal to a rubbery matrix can create a variety of surprising elastic effects. We derive a F\"{o}ppl-von K\'{a}rm\'{a}n type model for a very thin nematic elastomer, based on a phenomenological free energy. The model couples the order parameter to the elastic degrees of freedom of the plate. There are two categories of cross-linking which we explore: cross-linking in the isotropic phase, and cross-linking in the nematic phase. We consider the problem of wrinkling in scenarios of annular and rectangular sheets with tensile boundary conditions, where confinement causes a classical elastomer to buckle out-of-plane into a wrinkled configuration.