title: Geometry of thin nematic elastomer sheets.
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.
authors.affiliation: Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Hillel
authors.initials: H
authors.lastname: Aharoni
authors.affiliation: Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Eran
authors.initials: E
authors.lastname: Sharon
authors.affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Raz
authors.initials: R
authors.lastname: Kupferman