Journal
SOFT MATTER
Volume 10, Issue 34, Pages 6382-6386Publisher
ROYAL SOC CHEMISTRY
DOI: 10.1039/c4sm00845f
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Funding
- NSF [DMR-0846582]
- ARO [W911NF-11-1-0080]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0846582] Funding Source: National Science Foundation
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We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified. With this connection, we study the problem of choosing an optimal pattern of growth for a prescribed developable surface, finding a fundamental trade-off between optimal design and the accuracy of the resulting shape which can be quantified by the length along which an edge should be identified.
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