Facets and Folds: A model for fragmentation kinetics of crumpled thin sheets*

As a confined thin sheet crumples, a unique arrangement of sharp ridges emerges, delineating approximately flat facets. Viewed collectively, this mosaic of ridges and facets exhibits striking statistical reproducibility - the total length traced out by ridges, for instance, has been shown to grow logarithmically with the number of crumpling and unfolding repetitions. Here, we explore the correspondence between crumpling and a general fragmentation process. We identify a physical model for the evolution of facet area distribution in crumpled sheets that captures a wide range of data samples with a single variable parameter. We then demonstrate the capacity of this model to reproduce experimental observations such as the characteristic logarithmic scaling of total ridge length, thereby supplying a missing physical basis for the observed phenomenon.