Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913275056226304 |
|---|---|
| author | Bouck, Lucas Nochetto, Ricardo H. Yang, Shuo |
| author_facet | Bouck, Lucas Nochetto, Ricardo H. Yang, Shuo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02710 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation Bouck, Lucas Nochetto, Ricardo H. Yang, Shuo Numerical Analysis 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. |
| title | Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2210.02710 |