A fragmentation-based model for the crumpling of thin sheets

Crumpled systems are prime examples of complexity and disorder: As a thin sheet is confined, an intricate network of creases emerges spontaneously in regions of high localized stress. However, these systems can exhibit unexpected order: For example, the total length of creases which form in repeatedly crumpled Mylar sheets was found to grow logarithmically in the number of crumpling cycles. We propose a physical explanation for this behavior by considering crumpling as a fragmentation process, partitioning a sheet into facets whose area distribution evolves according to a kinetic equation for fragmentation. We develop a model for how the facet area distribution changes incrementally over one crumpling cycle based on geometric frustration between existing facets and the confining container. Our model captures the gradual compliance of the sheet which slows damage accumulation in agreement with the observed logarithmic scaling. We conclude by investigating these observations in a computational model of thin elastoplastic sheets, which enables deeper exploration of complex phenomena such as spatial damage evolution.