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arXiv · 2210.02710

Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation

Lucas Bouck·Ricardo H. Nochetto·Shuo Yang
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Abstract

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.

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Lucas Bouck, Ricardo H. Nochetto, Shuo Yang. 2022-10-06. Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation. https://arxiv.org/abs/2210.02710

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