Actuation of thin nematic elastomer sheets with controlled heterogeneity

TL;DR

This paper develops a theoretical framework for controlling the shape of thin nematic elastomer sheets through heterogenous director fields, enabling predictable shape changes upon temperature variation.

Contribution

It derives a two-dimensional metric constraint from a variational formulation, linking deformation to director heterogeneity, and proves its necessity and sufficiency for energy minimization.

Findings

The metric constraint characterizes feasible deformations.

Satisfying the constraint ensures near-minimal elastic energy.

The class of admissible deformations is broad and versatile.

Abstract

Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In this paper, we start from a variational formulation for the entropic elastic energy of liquid crystal elastomers and we derive an effective two-dimensional metric constraint, which links the deformation and the heterogeneous director field. Our main results show that satisfying the metric constraint is both necessary and sufficient for the deformation to be an approximate minimizer of the energy. We include several examples which show that the class of deformations satisfying the metric constraint is quite rich.