A model for the fragmentation kinetics of crumpled thin sheets

Kavli Affiliate: Shmuel M. Rubinstein

| First 5 Authors: Jovana Andrejevic, Lisa M. Lee, Shmuel M. Rubinstein, Chris H. Rycroft,

| Summary:

As a confined thin sheet crumples, it spontaneously segments into flat facets
delimited by a network of ridges. Despite the apparent disorder of this
process, statistical properties of crumpled sheets exhibit striking
reproducibility. Experiments have shown that the total crease length accrues
logarithmically when repeatedly compacting and unfolding a sheet of paper.
Here, we offer insight to this unexpected result by exploring the
correspondence between crumpling and fragmentation processes. We identify a
physical model for the evolution of facet area and ridge length distributions
of crumpled sheets, and propose a mechanism for re-fragmentation driven by
geometric frustration. This mechanism establishes a feedback loop in which the
facet size distribution informs the subsequent rate of fragmentation under
repeated confinement, thereby producing a new size distribution. We then
demonstrate the capacity of this model to reproduce the characteristic
logarithmic scaling of total crease length, thereby supplying a missing
physical basis for the observed phenomenon.

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