Theory of Liquid Crystal Elastomers: From Polymer Physics to Differential Geometry

Abstract

In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation 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.

References in corpus (4)

• Elastic theory of unconstrained non-Euclidean plates
• Encoding Gaussian curvature in glassy and elastomeric liquid crystal polymer networks
• Programming complex shapes in thin nematic elastomer and glass sheets
• Metric theory of nematoelastic shells

Cited by in corpus (12)

• Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals
• Tunable wrinkling of thin nematic liquid crystal elastomer sheets
• Actuation of thin nematic elastomer sheets with controlled heterogeneity
• Contrasting bending energies from bulk elastic theories
• A blend of stretching and bending in nematic polymer networks
• Dilation-invariant bending of elastic plates, and broken symmetry in shells
• Quadratic-stretch elasticity
• Some observations on variational elasticity and its application to plates and membranes
• A ribbon model for nematic polymer networks
• Bending and Stretching in a Narrow Ribbon of Nematic Polymer Networks
• Ridge approximation for thin nematic polymer networks
• Work and Activation in a Nematic Polymer Network Ribbon