Shape programming for narrow ribbons of nematic elastomers

TL;DR

This paper develops new one-dimensional models for nematic elastomer ribbons with spontaneous curvature and twist, using $ ext{Gamma}$-convergence, to analyze shape selection including helicoid-like configurations.

Contribution

It introduces a rigorous derivation of simplified models for nematic elastomer ribbons from 3D elasticity, focusing on shape control and novel configurations.

Findings

Helicoid-like shapes are possible alternatives to spiral ribbons.

New models predict shape outcomes based on nematic director textures.

The approach provides a foundation for designing shape-programmable elastomer ribbons.

Abstract

Using the theory of $\Gamma$-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e. ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons.