Physicists have worked out a universal law for how objects shatter

A dropped plate, a broken sugar cube, and a broken glass all seem to follow the same laws of physics when it comes to how many pieces of a given size they will break into.

For decades, researchers have known that there is something universal about the process of fragmentation, where an object breaks into many pieces when dropped or hit. If you count how many fragments there are of each possible size and plot this distribution, it will have the same shape regardless of the object that crashed. Emmanuel Willermo at the University of Aix-Marseille in France, derived an equation to explain this form, effectively formulating a universal law for how things break.

Instead of focusing on details how cracks appear in an object before it fragments, he took a more reduced approach. Villermo considered all possible sets of fragments into which an object could break. Some sets will include very specific results, such as a vase breaking into four equal pieces. He chose the most likely set with the highest entropy, which showed random and irregular failures. This is similar to how many laws concerning large ensembles of particles were derived in the 19th century.^th centuries, he says. In addition, Villermo used a law of physics that describes changes in the overall density of fragments during the destruction of an object that he and his colleagues had previously discovered.

Together, these two ingredients allowed him to derive a simple equation that predicted how many fragments of each size would be produced when an object collapsed. To see how well it worked, Willermo compared it to a variety of past experiments with broken glass grates, dry spaghetti, plates, ceramic tubes and even plastic fragments in the ocean and waves crashing on choppy seas. Overall, the way fragmentation appeared in each of these scenarios was consistent with his new law, reflecting the ubiquitous graph shape the researchers had seen before.

He also conducted a series of experiments in which he broke a sugar cube by dropping an object on it from different heights. “It was a summer project with my daughters. I did it a long time ago when my kids were little, and then I went back to the data because it illustrated my point well,” says Willermo. The equation doesn't work in cases where there is no randomness and the fragmentation process is too regular, such as when a stream of liquid breaks up into many droplets of the same size, following the deterministic laws of fluid physics, and in some cases where the fragments interact with each other during the destruction, he says.

Ferenc Kuhn from the University of Debrecen in Hungary say that since the graph form explained by Willermo's analysis is so common, it is not surprising that it follows from a more important principle. At the same time, it's surprising how broadly it works and how it can be modified in some cases where there are additional constraints, such as in plastic, where cracks can sometimes “heal,” he says.

Fragmentation is not just an interesting physics problem. A better understanding of this could have real implications for how energy is spent breaking down ore in industrial productionfor example, or how we prepare for rockfalls, which are increasingly occurring in mountainous regions as global temperature is risingSali Kuhn.

In the future, Kuhn says, it may be interesting to look at the distribution of not only the size of the fragments, but also their shape. In addition, the question remains what the smallest possible fragment size could be, says Villermo.