| Rim curvature anomaly in thin conical sheets revisited. | |
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MedLine Citation:
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PMID: 22304207 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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This paper revisits one of the puzzling behaviors in a developable cone (d-cone), the shape obtained by pushing a thin sheet into a circular container of radius R by a distance η. The mean curvature was reported to vanish at the rim where the d-cone is supported. We investigate the ratio of the two principal curvatures versus sheet thickness h over a wider dynamic range than was used previously, holding R and η fixed. Instead of tending toward 1 as suggested by previous work, the ratio scales as (h/R)^{1/3}. Thus the mean curvature does not vanish for very thin sheets as previously claimed. Moreover, we find that the normalized rim profile of radial curvature in a d-cone is identical to that in a "c-cone" which is made by pushing a regular cone into a circular container. In both c-cones and d-cones, the ratio of the principal curvatures at the rim scales as (R/h)^{5/2}F/(YR^{2}), where F is the pushing force and Y is the Young's modulus. Scaling arguments and analytical solutions confirm the numerical results. |
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Authors:
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Jin W Wang |
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Publication Detail:
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Type: JOURNAL ARTICLE Date: 2011-12-12 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 84 ISSN: 1550-2376 ISO Abbreviation: - Publication Date: 2011 Dec |
Date Detail:
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Created Date: 2012-2-6 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: - |
Other Details:
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Languages: ENG Pagination: 066603 Citation Subset: - |
Affiliation:
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James Franck Institute and Department of Physics, University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, USA. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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