Simulations of crumpling across confinement geometries

From cell membranes to tectonic plates, crumpling is the result of geometric incompatibility between a thin sheet and external confinement. It's been shown that crumpling statistics progress predictably, and crumpling occurs when planar facets of a sheet fragment into smaller facets. This progression is a robust function of the geometric confinement parameter and the number of compression cycles the sheet undergoes. This fragmentation model, however, has only been analyzed in the specific context of axially compressed sheets. Through simulations and comparison to experimental data, we demonstrate that the fragmentation model for crumpling applies to thin sheets crumpled via several different confinement geometries, including radial compression and cylindrical twisting. This suggests crumpling could be described universally if the correct confinement parameter can be identified.