A plate theory for nematic liquid crystalline solids

TL;DR

This paper develops a two-dimensional plate theory for nematic liquid crystalline solids, capturing their elastic and shape-changing behaviors under various stimuli and constraints.

Contribution

It introduces a Föppl-von Kármán-type model for nematic plates that accounts for director rotation and natural shape changes, extending existing theories.

Findings

Model applies to thin nematic bodies under optothermal and mechanical loads.

Reversible natural shape changes can be stress-free or blocked, inducing internal stresses.

Framework accommodates a wide range of problems in nematic solid mechanics.

Abstract

We derive a F\"{o}ppl-von K\'{a}rm\'{a}n-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustration, we consider certain reversible natural shape changes in simple systems which are stress free, and their counterparts, where the natural deformations are blocked and internal stresses appear. More general problems can be addressed within the same framework.