A ribbon model for nematic polymer networks
arXiv:2112.14671 · doi:10.1007/s10659-022-09900-9
Abstract
We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions.
arXiv commentPublished version
References in corpus (15)
- Elastic theory of unconstrained non-Euclidean plates
- Disclination-mediated thermo-optical response in nematic glass sheets
- Blueprinting Nematic Glass: Systematically Constructing and Combining Active Points of Curvature for Emergent Morphology
- "Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods
- A non-linear rod model for folded elastic strips
- Photomechanical coupling in photoactive nematic elastomers
- A plate theory for nematic liquid crystalline solids
- Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"
- Elasticity and Fluctuations of Frustrated Nano-Ribbons
- Tube Model for the Elasticity of Entangled Nematic Rubbers
- Theory of Liquid Crystal Elastomers: From Polymer Physics to Differential Geometry
- A blend of stretching and bending in nematic polymer networks
- Translation and interpretation of Michael Sadowsky's paper "Theory of elastically bendable inextensible bands with applications to the Möbius band"
- Translation of Michael Sadowsky's paper "The differential equations of the Möbius band"
- Ridge approximation for thin nematic polymer networks