Mechanical response of a self avoiding membrane: fold collisions and the birth of conical singularities

Abstract

An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex network of highly deformed crescent-like regions joined by line ridges. Previous studies have focused on the onset of the crumpled state by analyzing the mechanical response and stability of a conical dislocation, while others have simulated the highly packed regime neglecting the importance of the connectivity of the membrane. Here we show, through a combination of experiments, numerical simulations, and analytic approach, that the emergence of new regions of high stretching is a generic outcome when a self avoiding membrane is subject to a severe geometrical constraint. We demonstrate that, at moderate packing fraction, interlayer interactions produce a response equivalent to the one of a thicker membrane that has the shape of the deformed one. Evidence is found that friction plays a key role stabilizing the folded structures.

10 pages

References in corpus (2)

• Morphological Phases of Crumpled Wire
• Wrinkling of a bilayer membrane

Cited by in corpus (6)

• Plasticity and Aging of Folded Elastic Sheets
• Cutting holes in bistable folds
• Dilation-invariant bending of elastic plates, and broken symmetry in shells
• Simulation of crumpled sheets via alternating quasistatic and dynamic representations
• Wrinkling and developable cones in centrally confined sheets
• Rim curvature anomaly in thin conical sheets revisited