Stretching Ridges in a Crumpled Elastic Sheet

A. E. Lobkovsky, S. Gentges, T. A. Witten
The James Franck Institute
The University of Chicago
5640 South Ellis Avenue Chicago, Illinois 60637

Hao Li, NEC Research Institute

David Morse, ITP, UC Santa Barbara

Strong deformation of a sheet of solid material often leads to a crumpled state having sharp points of high curvature. We numerically demonstrate a scaling property governing the crumpled state by examining the ridges joining pairs of sharp points ina 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 a thin elastic sheet should be concentrated in ridges that obey these scaling laws.