Modeling and Simulation of Liquid Crystal Elastomers

TL;DR

This paper develops a continuum model for nematic liquid crystal elastomers, incorporating elastic and liquid crystalline energies, and demonstrates its effectiveness through numerical simulations that replicate experimental shape-changing behaviors.

Contribution

The paper introduces a novel continuum model and numerical scheme for simulating the dynamic behavior of nematic liquid crystal elastomers, capturing shape changes and order parameter evolution.

Findings

Model accurately reproduces experimental shape dynamics

Simulation tracks evolution of the order parameter tensor

Numerical scheme is stable and efficient

Abstract

We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation are used, within a Lagrangian framework, to obtain the equations of motion. The free energy consists of both elastic and liquid crystalline contributions, each of which is a function of the material displacement and the orientational order parameter. The model gives dynamics for the material displacement, the scalar order parameter and the nematic director, the latter two of which correspond to the orientational order parameter tensor. Our simulations are carried out by solving the governing equations using an implicit-explicit scheme and the Chebyshev polynomial method. The simulations show that the model can successfully capture the shape changing dynamics of LCEs that have been observed in experiments, and also track the evolution of the order parameter tensor.