Dr. Lee then opened the folded sheet and subjected it to the usual regimen of crumpling, recrumpling and recrumpling some more. “Even after just a single crumple, the facets closely resembled the distribution predicted by our model,” said Dr. Lee, who is now doing research and development at ThermoFisher Scientific. The facets quickly fell in line with the classic fragmentation distribution, and thereafter followed the same universal evolution.
This shows how, in a fragmentation process, any special pattern of fragment sizes is rapidly washed out — vanishing after a single crumple, in the case of the grid folding. Technically speaking, this means the steady-state distribution of sizes is a “strong attractor,” a state toward which a system tends to evolve.
This further explained why the overall “mileage” would exhibit universal behavior and predict the evolution of the crease network.
However, one piece of the puzzle was still missing: an explanation of the physical dynamics.
“We found our answer by incorporating some geometry,” Ms. Andrejević said. Given a sheet’s crease pattern after, say, nine crumples, and given the geometry of its confinement when crumpled again, the researchers could predict how much new damage would occur during the 10th crumple — that is, what the sheet would look like after enduring yet another round of “geometric frustration.”
The rules of crumpling
By the end of their summer research, in July, Ms. Andrejević and Dr. Rycroft sent their theory — in a document named “crumpling_math_model” — to Dr. Rubinstein. “I was blown away,” Dr. Rubinstein recalled.
In fact, they were all surprised that fragmentation theory proved so effective. “To the best of our knowledge this is the first application of such concepts to describe crumpling,” the authors wrote in their paper.