Properties of Ridges in Elastic Membranes

TL;DR

This paper investigates the properties of ridges in crumpled elastic membranes, analyzing their energy ratios, response to perturbations, and buckling behavior to understand their stability and morphology.

Contribution

It extends previous models by examining perturbations, linear response, and buckling, providing new insights into ridge stability in crumpled sheets.

Findings

Virial theorem predicts energy ratio of bending to stretching.

Ridge energy can change by a finite fraction before buckling.

Perturbations distinguish crumpled ridges from isolated ones.

Abstract

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.