March 1, 2002

Physicists find paper keeps crumpling

University physicists Thomas Witten and Sidney Nagel have been investigating where energy is stored in thin sheets of Mylar when work is performed on them by crumpling. They find the ability of a simple sheet of paper to resist further crumpling fascinating. "You realize that what you are holding is 75 percent air," Nagel said.

The researchers have been considering the energy-storing problem in large, very thin metallic sheets of Mylar since the mid-'90s, when the research began with two undergraduates in the College doing the experimentation. However, as the students began to get unexpected results, Witten, professor in the department of physics, took notice.

To investigate the process, researchers crumpled sheets of Mylar, placed them in a plastic tube, and applied a weight to them, then observing how the sheets compressed over time. Witten and Nagel, the Stein-Freiler Distinguished Service Professor of Physics, expected to be able to discover a simple empirical law that described the process of crumpling.

They expected the law to be independent of the material used, except for variety in the size of forces involved. However, they have had difficulty finding such a law, since the height of the crumpled Mylar did not asymptotically approach a minimum value as they expected it would. "We waited three weeks, until we got bored," Nagel said.

By this time they had been sure that the paper would have reached maximum compression, but it was continuing to sink lower, the reason for which they aren't certain of. "We all expected it to stop compressing," Witten said.

According to the researchers, the important thing to understand with the paper balls is where the energy is stored in the crumpled piece of paper. The problem of understanding where the energy goes on the local level is not difficult, for the individual ridges and peaks that make up the crumpled paper are very well understood, the stuff of fairly elementary physics, which should make finding the total energy a fairly simple problem as well.

Understanding individual peaks and ridges, researchers should be able to find the average size and number of peaks and ridges per unit of area, calculate the contributed energies by simple methods, and then multiply to find the energy in the entire sheet. However, the nature of crumpling defies such an attempt.

"The big puzzle is why the pattern is so heterogeneous," Witten said. Crumpling a normal piece of notepaper (not too tightly, for their theories do not work under very great pressures) yields ridges of widely varying sizes connecting the peaks. This variety makes it difficult to find any meaningful average over the sheet or to understand which ridges and peaks are most important.

Witten and Nagel suspect that most of the energy in a crumpled paper is in the long ridges which have a lower energy density, as opposed to in the higher density peaks that cover more area.

Witten and Nagel see crumpling in many things, from tectonic plates and packing paper to car wrecks and wrinkles in clothing. According to Witten and Nagel, despite the various materials and the magnitudes of forces involved, upon inspection, the crumpling zones look similar and are all made of peaks and ridges. By better understanding where the energy goes in a paper crumpled and tossed into the trash can, researchers may be able to better understand what is going on in other instances of crumpling.