REVISTA DYNA NEW TECHNOLOGIES

The law proposed by physicist Emmanuel Villermaux, from Aix-Marseille University and the University Institute of France, is built on two key ideas: a principle of “maximal randomness,” which states that a violent breakup tends to produce the most chaotic distribution of fragments, and a conservation rule that constrains how the total size of all pieces can be distributed. When these two ingredients are combined, they yield a compact equation that predicts the characteristic power-law shape of the fragment size distribution and links its exponent to the dimensionality of the original object.

Villermaux tested the theory against a large body of experimental data collected over decades from shattering glass rods, ceramic plates, fragile tubes, and even plastic debris broken up by ocean waves, as well as his own experiments dropping and crushing single sugar cubes. Across this wide range of systems, the predicted distributions closely matched the observed ones, suggesting that the same statistical mechanism governs fragmentation whenever the process is sufficiently disordered and crack paths are not strongly constrained.

The new law, however, is not universal in an absolute sense: it works best for random, violent breakups, such as a tumbler smashing on the floor, but fails when materials are very soft and deform rather than fracture, or when breakup follows a highly regular pattern, like a liquid jet breaking into nearly identical droplets due to surface tension. Even so, the framework is promising for practical problems, from reducing the huge energy cost of crushing rock in mining, to improving models of rockfalls in warming mountain regions, to understanding how large plastic items are ground down into microplastics in the environment. Researchers now want to extend the theory to include fragment shapes and to identify what ultimately limits the smallest fragment size that real materials can produce.