Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics

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Science  23 Feb 2007:
Vol. 315, Issue 5815, pp. 1116-1120
DOI: 10.1126/science.1135994

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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.

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