Physicists Discover Universal Law Governing How Objects Fracture

The physics behind a dropped plate, a crumbled sugar cube, and a shattered glass shows striking similarities regarding how many pieces result from each object breaking.

For decades, researchers have recognized a universal behavior related to fragmentation, where objects break apart upon falling or colliding. If one counts the fragments of varying sizes and plots their distribution, a consistent shape emerges regardless of the object that is broken. Emmanuel Villemaux from the University of Aix-Marseille in France has formulated equations to illustrate these shapes, thereby establishing universal laws of fragmentation.

Instead of concentrating on the appearance of cracks leading to an object’s breakup, Villermaux employed a broader approach. He considered all potential fragment configurations that could result in shattering. Some configurations produce precise outcomes, such as a vase breaking into four equal parts; however, he focused on capturing the most probable set that represents chaotic breakage, namely the one with the highest entropy. This mirrors methods used to derive laws concerning large aggregates of particles in the 19th century, he notes. Villermaux also applied the principles of physics that govern changes in fragment density during shattering, knowledge previously uncovered by him and his colleagues.

By integrating these two elements, they succeeded in deriving a straightforward equation that predicts the size distribution of fragments in a broken object. To verify its accuracy, Villermaux compared it against a number of earlier experiments involving glass rods, dry spaghetti, plates, ceramic tubes, and even fragments of plastic submerged in water and waves crashing during stormy weather. Overall, the fragmentation patterns observed in each of these experiments conformed to his novel law and reflected the universal distribution shapes previously noted by researchers.

He also experimented by dropping objects from varying heights to crush sugar cubes. “This was a summer endeavor with my daughters. I had done it a long time ago when they were young, and later revisited the data to further illustrate my concept,” Villermaux explains. He observes that this equation fails to hold when randomness is absent, or the fragmentation process is overly uniform, as occurs when a liquid stream divides into uniform droplets based on the deterministic rules of fluid dynamics, or in instances when fragments engage with each other during fragmentation.

Mr. Ferenc and his colleagues at the University of Debrecen in Hungary argue that the graphical pattern highlighted in Villermaux’s analysis is so fundamentally universal that it may derive from a more extensive principle. Simultaneously, they express surprise at how broadly applicable it is, as well as its adaptability to accommodate specific variations, such as in plastics where cracking can be “healed.”

Fragmentation is not merely a captivating challenge in physics; a deeper understanding could significantly impact energy expenditures in mining operations or guide preparations for increasing rockfalls in mountainous areas as global temperatures tend to rise, Kuhn remarks.

Looking ahead, it may prove beneficial to explore not only the sizes of the fragments but also their shape distributions, suggests Kuhn. Additionally, identifying the smallest conceivable size of a fragment remains an unresolved issue, according to Villermaux.