Negative Gaussian curvature from induced metric changes.
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.
The Rockefeller University, Center for Studies in Physics and Biology, 1230 York Avenue, New York, New York 10065, USA.
Carl D
CD
Modes
Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
Mark
M
Warner