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Negative Gaussian curvature from induced metric changes

Carl D. Modes and Mark Warner
Phys. Rev. E 92, 010401(R) – Published 21 July 2015

Abstract

We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated—so-called “anticones.” We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.

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  • Received 19 February 2015

DOI:https://doi.org/10.1103/PhysRevE.92.010401

©2015 American Physical Society

Authors & Affiliations

Carl D. Modes1 and Mark Warner2

  • 1The Rockefeller University, Center for Studies in Physics and Biology, 1230 York Avenue, New York, New York 10065, USA
  • 2Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

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Issue

Vol. 92, Iss. 1 — July 2015

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