Properties of ridges in elastic membranes

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 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.