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

10/06/2022
by   Lucas Bouck, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/10/2022

Convergent FEM for a membrane model of liquid crystal polymer networks

We design a finite element method (FEM) for a membrane model of liquid c...
research
08/10/2021

Simulating Self-Avoiding Isometric Plate Bending

Inspired by recent results on self-avoiding inextensible curves, we prop...
research
11/11/2019

A structure-preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals

We consider the one-constant Landau - de Gennes model for nematic liquid...
research
12/10/2021

A nonconforming finite element method for an elliptic optimal control problem with constraint on the gradient

This article is concerned with the nonconforming finite element method f...
research
06/14/2021

A scalable multi-step least squares method for network identification with unknown disturbance topology

Identification methods for dynamic networks typically require prior know...
research
05/13/2021

Finite element algorithms for nonlocal minimal graphs

We discuss computational and qualitative aspects of the fractional Plate...
research
11/02/2020

LDG approximation of large deformations of prestrained plates

A reduced model for large deformations of prestrained plates consists of...

Please sign up or login with your details

Forgot password? Click here to reset