Scaling properties of stretching ridges in a crumpled elastic sheet

Alex Lobkovsky, James Franck Institute, University of Chicago, Chicago IL 60637.

Sharon Gentges

Hao Li, Present address: NEC Research Institute, 4 Independence Way, Princeton, NJ 08540

David Morse, Institute for Theoretical Physics, University of California, Santa Barbara CA 93106.

T.A. Witten

ABSTRACT of paper accepted in Science 9/95

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 examining the {\it 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 $X^{1/3}$. Remarkably, it consists of similar amounts of bending and stretching energy. This energy becomes concentrated in a fraction of the sheet that decreases as $X^{-1/3}$. Despite this concentration, the local strain in the ridge decreases, as $X^{-2/3}$. Nearly all the deformation energy in thin, crumpled elastic sheets should be concentrated in ridges that obey these scaling laws.

University of Chicago Materials Center