We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of the 2D membrane model from 3D rubber elasticity. We construct approximate solutions with point defects. We design a finite element method with regularization, and propose a nonlinear gradient flow with Newton inner iteration to solve the non-convex discrete minimization problem. We present numerical simulations of practical interests to illustrate the ability of the model and our method to capture rich physical phenomena.

We develop a Q-tensor model of nematic liquid crystals occupying a surface which represents a fixed fluidic material film in space. In addition to the evolution due to Landaude Gennes energy the model includes a tangent viscous flow along the surface. The coupling of a two-dimensional flow and a three-dimensional Q-tensor dynamics is derived from the generalized Onsager principle following the Beris-Edwards system known in the flat case. The main novelty of the model is that it allows for a flow of an arbitrarily oriented liquid crystal so the Q-tensor is not anchored to the tangent plane of the surface. Several numerical experiments explore kinematical and dynamical properties of the novel model.