Geometry of Thin Nematic Elastomer Sheets

TLDR: In this article, the intrinsic geometry of a thin sheet of nematic elastomer is described and an expression for the metric induced by general nematic director fields is derived, and an explicit recipe for how to construct any surface of revolution using this method is provided.

Abstract: A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this Letter, we describe the intrinsic geometry of such a sheet and derive an expression for the metric induced by general nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit recipe for how to construct any surface of revolution using this method. Finally, we show that by inscribing a director field gradient across the sheet's thickness, one can obtain a nontrivial hyperbolic reference curvature tensor, which together with the prescription of a reference metric allows dictation of actual configurations for a thin sheet of nematic elastomer.