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Science 1 December 1995:
Vol. 270. no. 5241, pp. 1482 - 1485
DOI: 10.1126/science.270.5241.1482
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Reports

Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet

Alex Lobkovsky,  Sharon Gentges,  Hao Li (1),  David Morse,  T. A. Witten (2)

Strong deformation of a sheet of solid material often leads to a crumpled state having sharp points of high curvature. A scaling property governing the crumpled state has been numerically demonstrated by an examination of the ridges joining pairs of sharp points in a range of simple geometries of variable size. As the linear size X increases sufficiently, the deformation energy grows as X and consists of similar amounts of bending and stretching energy. The deformation energy becomes concentrated in a fraction of the sheet that decreases as X. Despite this concentration, the local strain in the ridge decreases as X. Nearly all the deformation energy in thin, crumpled elastic sheets was found to be concentrated in ridges that obey these scaling laws.


A. Lobkovsky, S. Gentges, H. Li, T. A. Witten, James Franck Institute, University of Chicago, Chicago, IL 60637, USA. World Wide Web: http://arnold.uchicago.edu/MRSEC
D. Morse, Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA.
(1) Present address: NEC Research Institute, Incorporated, 4 Independence Way, Princeton, NJ 08540, USA.
(2) To whom correspondence should be addressed. E-mail: t-witten{at}uchicago.edu


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Science. ISSN 0036-8075 (print), 1095-9203 (online)