Scaling relation for a compact crumpled thin sheet

A high-pressure chamber was designed to study crumpling beyond the power-law regime. Preceded by a smooth transition, the crumpled ball that characterizes the high-pressure state contains less than 50% air and exhibits separate ordered domains. All data for different sheet thicknesses, sizes, and numbers were found to collapse to a master line when using volume ratio and pressure as the plotting parameters, which suggests the existence of a scaling relation. Based on these findings, we deduced a bundled-layer model that could consistently explain six outstanding properties at both low and high pressures. This successful union of theory and experiment has strong bearings on other soft-matter systems where similar changes in mechanical response are also linked to reorganization of structure.