November 30, 2023

Dr. Lee then opened the folded sheet and subjected it to the usual crumple, re-shred, and re-crumple scheme. “Even after just one squeeze, the facets were very similar to the distribution our model predicted,” said Dr. Lee, who is now researching and developing at ThermoFisher Scientific. The facets quickly agreed with the classical fragmentation distribution and then followed the same universal development.

This shows how, in a fragmentation process, any particular pattern of fragment sizes is quickly washed out – in the case of a grid fold, it disappears after a single crumple. Technically speaking, this means that the stationary size distribution is a “strong attractor”, a state that a system tends to develop into.

This further explained why the total mileage would exhibit universal behavior and predict the evolution of the kink network.

One piece of the puzzle was still missing: an explanation of the physical dynamics.

“We found our answer by including geometry,” said Ms. Andrejević. Given the crease pattern of a sheet after, say, nine wrinkles and the geometry of its containment when wrinkled again, the researchers were able to predict how much new damage would occur during the 10th wrinkle – that is, what the sheet would look like after holding out another round “more geometric.” Frustration”.

At the end of their summer research in July, Ms. Andrejević and Dr. Rycroft presented their theory – in a document called “crumpling_math_model” – to Dr. Rubinstein. “I was overwhelmed,” recalled Dr. Rubinstein.

In fact, they were all surprised that fragmentation theory turned out to be so effective. “To the best of our knowledge, this is the first time such concepts have been used to describe crumple,” the authors wrote in their article.