Universal deformations of ideal liquid crystal elastomers

TL;DR

This paper explores universal deformation behaviors in liquid crystal elastomers, extending understanding from simple to complex inhomogeneous deformations through modeling and classical elasticity theory.

Contribution

It introduces a framework for analyzing complex inhomogeneous deformations in liquid crystal elastomers using Ericksen's universal deformation theory.

Findings

Universal deformations exist for complex inhomogeneous cases

Modeling of balloon inflation and cavitation in liquid crystal elastomers

Extension of classical elasticity results to liquid crystal elastomers

Abstract

Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of homogenous deformations. This paper investigates soft behavior in complex inhomogeneous deformations. We model these materials as hyperelastic, isotropic, incompressible solids and exploit the seminal work of Ericksen, who established the existence of non-trivial universal deformations, those that satisfy the equations of equilibrium in every hyperelastic, isotropic, incompressible solid. We study the inflation of spherical and cylindrical balloons, cavitation and bending.