Eur. Phys. J. E (2017) 40: 76
https://doi.org/10.1140/epje/i2017-11569-5

Regular Article

Theory of liquid crystal elastomers and polymer networks

Connection between neoclassical theory and differential geometry

Liquid Crystal Institute, Kent State University, 44242, Kent, OH, USA

^* e-mail: jselinge@kent.edu

Received: 21 May 2017
Accepted: 6 September 2017
Published online: 18 September 2017

Abstract

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.