Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
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- 23 February 2007
- journal article
- other
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 315 (5815), 1116-1120
- https://doi.org/10.1126/science.1135994
Abstract
The connection between a surface's metric and its Gaussian curvature (Gauss theorem) provides the base for a shaping principle of locally growing or shrinking elastic sheets. We constructed thin gel sheets that undergo laterally nonuniform shrinkage. This differential shrinkage prescribes non-Euclidean metrics on the sheets. To minimize their elastic energy, the free sheets form three-dimensional structures that follow the imposed metric. We show how both large-scale buckling and multiscale wrinkling structures appeared, depending on the nature of possible embeddings of the prescribed metrics. We further suggest guidelines for how to generate each type of feature.Keywords
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