Properties of Ridges in Elastic Membranes

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

When a thin elastic sheet is confined to a region much smaller than its size the morphology of the resulting crumpled membrane is a network of straight ridges or folds that meet at sharp vertices. A virial theorem predicts the ratio of the total bending and stretching energies of a ridge. Small strains and curvatures persist far away from the ridge. We discuss several kinds of perturbations that distinguish a ridge in a crumpled sheet from an isolated ridge studied earlier (A.~E. Lobkovsky, Phys. Rev. E. {\bf 53} 3750 (1996)). Linear response as well as buckling properties are investigated. We find that quite generally, the energy of a ridge can change by no more than a finite fraction before it buckles.