CUED Publications database

Nematic director fields and topographies of solid shells of revolution

Warner, M and Mostajeran, C (2018) Nematic director fields and topographies of solid shells of revolution. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474. 20170566-. ISSN 1364-5021

Full text not available from this repository.

Abstract

©2018 The Author(s) Published by the Royal Society. All rights reserved. We solve the forward and inverse problems associated with the transformation of flat sheets with circularly symmetric director fields to surfaces of revolution with non-trivial topography, including Gaussian curvature, without a stretch elastic cost. We deal with systems slender enough to have a small bend energy cost. Shape change is induced by light or heat causing contraction along a non-uniform director field in the plane of an initially flat nematic sheet. The forward problem is, given a director distribution, what shape is induced? Along the way, we determine the Gaussian curvature and the evolution with induced mechanical deformation of the director field and of material curves in the surface (proto-radii) that will become radii in the final surface. The inverse problem is, given a target shape, what director field does one need to specify? Analytic examples of director fields are fully calculated that will, for specific deformations, yield catenoids and paraboloids of revolution. The general prescription is given in terms of an integral equation and yields a method that is generally applicable to surfaces of revolution.

Item Type: Article
Uncontrolled Keywords: curvature elastomers glasses nematic shape
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 24 Jan 2018 20:06
Last Modified: 28 Nov 2019 02:22
DOI: 10.1098/rspa.2017.0566