Numerical Studies on Membrane Crumpling

In this Thesis crumpling of thin sheets is explored when they are confined into a small volume by external forcing. To this end a simulation model based on a discrete element method is constructed. The Thesis begins with an introductory part reviewing the related elasticity theory and previous results on the properties of relevant geometric structures, ridges and cones, which appear in crumpled sheets. Results are reported for elastic and plastic thin sheets, and elastic sheets with self adhesion. Crumpling of elastic sheets was found to exhibit deterministic features and efficient packing of the sheet. Real materials at macroscopic scale are, however, elasto-plastic. By including plasticity we found that the crumpling process became random in agreement with everyday experience, and found that in contrast with intuitive expectations it is harder to crumple a plastic sheet. At microscopic scales van der Waals interactions and thermal fluctuations are essential for conformations of thin sheets. These effects are included in the simulations realized by Langevin dynamics. An intriguing question of whether adhesive interactions and thermal fluctuations would induce crumpling, even in the absence of external forcing, is discussed. Stability of microscopic membranes is explained in terms of membrane stiffness, adhesion strength and temperature.