Reduced membrane model for liquid crystal polymer networks: Asymptotics and computation

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 nonconvex stretching energy. We show a formal asymptotic derivation of the 2 D membrane model from 3 D 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.