CONVERGENT FEM FOR A MEMBRANE MODEL OF LIQUID CRYSTAL POLYMER NETWORKS\ast

被引：2

作者：

Bouck, Lucas ^{[1
]}

Nochetto, Ricardo H. ^{[1
,2
]}

Yang, Shuo ^{[3
,4
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

[3] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China

[4] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2023年 / 61卷 / 06期

基金：

美国国家科学基金会;

关键词：

liquid crystal polymer networks; finite element method; membrane model; FINITE-ELEMENT APPROXIMATION; NEMATIC ELASTOMERS; RELAXATION; ACTUATION; SHEETS;

D O I：

10.1137/22M1521584

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We design a finite element method for a membrane model of liquid crystal polymer networks. This model consists of a minimization problem of a nonconvex stretching energy. We discuss properties of this energy functional such as lack of weak lower semicontinuity. We devise a discretization with regularization, propose a novel iterative scheme to solve the nonconvex discrete minimization problem, and prove stability of the scheme and convergence of discrete minimizers. We present numerical simulations to illustrate convergence properties of our algorithm and features of the model.

引用

页码：2887 / 2916

页数：30

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