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Phys Rev Lett. 2014 Dec 19;113(25):257801. Epub 2014 Dec 17.

Geometry of thin nematic elastomer sheets.

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Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.


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.

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