Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation
Numerical Analysis
2024-03-22 v2 Numerical Analysis
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.
Cite
@article{arxiv.2210.02710,
title = {Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation},
author = {Lucas Bouck and Ricardo H. Nochetto and Shuo Yang},
journal= {arXiv preprint arXiv:2210.02710},
year = {2024}
}