he Math and Physics of Breaking Spaghetti

It’s a little known fact, but spaghetti has been mystifying physicists for decades.

The reason why has to do with a puzzle about why the long, cylindrical dried pasta breaks the way it does when it is held at the ends and bent, where instead of breaking into two pieces at the point where the bend is greatest, the way that most solid, brittle materials of similar proportions will fracture, a strand of spaghetti will break into three or more pieces instead when bent.

Dustin at Smarter Every Day explains why the spaghetti-breaking conundrum is a really big deal in a 7 minute-long video:

There’s nothing like watching dry spaghetti break at a quarter-million frames per second!

The reason why we’re covering this topic today is because a group of mathematicians and mechanical engineers have teamed up to not only solve the puzzle of why dry spaghetti fractures the way that it does, but also how to manipulate spaghetti strands to break into just two pieces. The researchers, Ronald H. Heisser, Vishal P. Patil, Norbert Stoop, Emmanuel Villermaux, and Jörn Dunkel, explain why what might otherwise seem to be trivial work into the fracture dynamics of dry spaghetti noodles is significant in their recently published paper.

Fracture processes are ubiquitous in nature, from earthquakes to broken trees and bones. Understanding and controlling fracture dynamics remain one of the foremost theoretical and practical challenges in material science and physics. A well-known problem with direct implications for the fracture behavior of elongated brittle objects, such as vaulting poles or long fibers, goes back to the famous physicist Richard Feynman who observed that dry spaghetti almost always breaks into three or more pieces when exposed to large bending stresses. While bending-induced fracture is fairly well understood nowadays, much less is known about the effects of twist. Our experimental and theoretical results demonstrate that twisting enables remarkable fracture control by using the different propagation speeds of twist and bending waves.

MIT’s press release announcing the publication of the researchers’ paper in the Proceedings of the National Academy of Sciences reveals how mathematical analysis was able to accurately describe both how spaghetti breaks into three or more pieces under ordinary bending conditions, and how it might be additionally manipulated so that it would only break into two pieces:

Patil began to develop a mathematical model to explain how twisting can snap a stick in two. To do this, he generalized previous work by the French scientists Basile Audoly and Sebastien Neukirch, who developed the original theory to describe the “snap-back effect,” in which a secondary wave caused by a stick’s initial break creates additional fractures, causing spaghetti to mostly snap in three or more fragments.

Patil adapted this theory by adding the element of twisting, and looked at how twist should affect any forces and waves propagating through a stick as it is bent. From his model, he found that, if a 10-inch-long spaghetti stick is first twisted by about 270 degrees and then bent, it will snap in two, mainly due to two effects. The snap-back, in which the stick will spring back in the opposite direction from which it was bent, is weakened in the presence of twist. And, the twist-back, where the stick will essentially unwind to its original straightened configuration, releases energy from the rod, preventing additional fractures.

“Once it breaks, you still have a snap-back because the rod wants to be straight,” Dunkel explains. “But it also doesn’t want to be twisted.”

Just as the snap-back will create a bending wave, in which the stick will wobble back and forth, the unwinding generates a “twist wave,” where the stick essentially corkscrews back and forth until it comes to rest. The twist wave travels faster than the bending wave, dissipating energy so that additional critical stress accumulations, which might cause subsequent fractures, do not occur.

“That’s why you never get this second break when you twist hard enough,” Dunkel says.

The authors confirmed the analytical predictions with experimental data, where they constructed a rig to both twist and bend spaghetti strands to put the mathematical theory to the test.

And because they did, we now have a much better understanding of the structural mechanics of a material that we previously did not have, which opens the door to using materials with similar properties in real-world structural applications.

Or for that matter, to improve the structural performance of the next generation of spaghetti bridges!