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We design a finite element method (FEM) for a membrane model of liquidcrystal polymer networks (LCNs). This model consists of a minimization problemof a non-convex stretching energy. We discuss properties of this energyfunctional such as lack of weak lower semicontinuity. We devise adiscretization with regularization, propose a novel iterative scheme to solvethe non-convex discrete minimization problem, and prove stability of the schemeand convergence of discrete minimizers. We present numerical simulations toillustrate convergence properties of our algorithm and features of the model.

Convergent FEM for a membrane model of liquid crystal polymer networks