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

TL;DR

This study investigates how a self-avoiding elastic membrane deforms under severe confinement, revealing the formation of conical singularities and the role of friction and interlayer interactions in stabilizing folds.

Contribution

It combines experiments, simulations, and analysis to show that high stretching regions and conical singularities emerge naturally in confined membranes, highlighting the importance of connectivity and friction.

Findings

Emergence of high stretching regions with severe confinement

Interlayer interactions mimic thicker membrane responses

Friction stabilizes folded membrane structures

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.