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

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. In this article we study through a combination of experiments, numerical simulations, and analytic approaches the emergence of localized regions of high stretching when a self-avoiding membrane is subject to a severe geometrical constraint. Based on our experimental observations and numerical results we suggest that at moderate packing fraction interlayer interactions produce a response equivalent to that of a thicker membrane that has the shape of the deformed one. We find that new conical dislocations, coined satellite d-cones, appear as the deformed membrane further compactifies. When these satellite d-cones are born, a substantial relaxation of the mechanical response of the membrane is observed. Evidence is found that friction plays a key role in stabilizing the folded structures.