Scientists Propose Universal Law Explaining How Materials Break
A New Rule for How Objects Shatter
Why Physicists Study Broken Objects
When a plate slips or a glass shatters, most of us think only of the mess and the cost of replacing it. But to certain physicists, those scattered fragments are a puzzle worth pondering: why do broken objects produce such a wide range of piece sizes? Emmanuel Villermaux of Aix-Marseille University and the University Institute of France now proposes a simple, elegant rule that describes how materials fracture—whether brittle solids, falling droplets, or bursting bubbles.
Scientists have long believed that fragmentation follow a universal pattern. When the number of fragments within each size range is counted and plotted, the resulting distribution appears to take the same form, no matter what object has broken.
A Formula for Fragmentation
The Principle of Maximal Randomness
Villermaux began by examining the sheer chaos unleashed when an object shatters. He suggested that, in most situations, the outcome naturally favours the messiest and most irregular pattern—an idea he termed maximal randomness, reflecting nature's tendency to follow the simplest route.
The Conservation Law Behind Fragment Size Patterns
Yet, because chaos itself is bound by physical constraints, he incorporated a conservation law previously identified by his team. This hidden rule ensures that the overall distribution of fragment sizes—how many large pieces and how many small ones—cannot vary arbitrarily during breakage. By merging maximal randomness with this conservation principle, Villermaux formulated a universal law of fragmentation.
"A kinematic constraint applied to a maximal randomness principle infers both the power-law form of the fragment-size distribution and the value of its dimension-dependent exponent," he wrote in Physical Review Letters.
Testing the New Law
Matching a Century of Fragmentation Data
By bringing these two principles together, Villermaux was able to mathematically forecast the universal size pattern of fragments produced during a shattering event. His model proved an excellent match for decades' worth of fragmentation data involving everything from brittle solids to liquid structures.
Sugar Cube Experiments
He further demonstrated its accuracy in a simple yet clever experiment, crushing individual sugar cubes and precisely predicting the resulting fragment sizes based on the cube's three-dimensional geometry.
Limitations of the Model
Even so, the universal law does not apply to every form of breakage. It works best when an object fractures in a largely random manner, such as a glass vessel smashing on the floor. It performs less reliably when the material is too soft, like certain plastics, or when the breakup follows a more orderly pattern—for example, when surface tension causes a water stream to split into uniform droplets.
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