Paper view: Finally, clues to some of the mysteries of crumpling

It’s mind-bending but true: the average ball of crumpled paper is one of the most mysterious puzzles in physics.

PREMIUM

Researchers from Harvard University’s department of applied physics have been studying, for three years, what it is that makes crumpled paper so weight-resistant (there’s a reason it’s used as insulation for fragile objects), what makes it so unpredictable, and what makes it impossible to replicate.

First, the weight-resistance. The way it works, the researchers found, is that the more a sheet is crumpled, the more it resists further compression because the folds and ridges in the sheet turn it into a sort of fortress, each one acting as a tiny pillar to external resistance.

Meanwhile, it turns out that, like the snowflake, every piece of paper crumples in a different pattern. Even with the same sheet, that pattern is impossible to recreate.

It is possible to predict, however, and this has wide-ranging applications for devices such as processors and electrodes. The principles of crumpling sheets, essentially, could be used to more effectively utilise the surface areas of plastic and polymer-based materials (or anything that crumples).

After years of research, the Harvard study published in Nature Communications in 2021 was able to prove that the ridges in crumpled paper (and other materials that crumple) are shaped by a logarithmic pattern, where the ridges formed are longer in the beginning and much shorter by the end. Their data showed that fragmentation theory could successfully be used to predict its patterns.

Arriving at this finding was a painstaking, manual task. The patterns of the 24 test sheets of crumpled paper were so irregular that algorithms could not analyse them accurately for data. Researchers had to trace each ridge and surface across 24 separate sheets, physically, over days.

“What’s really motivating us is the bigger picture. Crumpling is a widespread phenomenon that occurs in many materials and is also the mechanism by which many materials fail — sometimes by design,” Jovana Andrejevic, a graduate student in applied physics in the School of Engineering and Applied Sciences at Harvard University, and lead author of the paper, told Harvard Magazine.

Crumple zones in cars are engineered so that energy from an impact is directed to, and absorbed in, the front and rear of the vehicle’s body. Similarly, crumpled sheets of graphene are being investigated for use as battery electrodes for their greater structural stability and because they offer more surface area for chemical reactions.

Why does paper crumple the way it does? The mechanics of it remain a mystery. The Harvard researchers are now refining their simulations to try to map how the physical forces at play cause the patterns they cause.