Voronoi Fracture | mysimulator.uk

Why glass shatters into jagged pieces, not neat cubes

When a brittle material like glass, ceramic or ice breaks, the crack pattern is not random noise — it follows the paths of least resistance through the material, which is closely modelled by a mathematical structure called a Voronoi diagram. Scatter a set of random points (representing tiny pre-existing flaws or stress concentrations in the material) across a surface, and partition the surface into regions where every point in a given region is closer to its own seed than to any other seed — those region boundaries look remarkably like the crack network you see in shattered glass or dried mud.

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This resemblance is not a coincidence: real fracture in a brittle material tends to propagate through the weakest, most stressed paths and to divide the impact energy roughly evenly outward from the point of impact, which is exactly the geometric property a Voronoi diagram captures — every boundary sits at the natural, equally-contested edge between two nearby stress centres.

Voronoi cell of seed point Pi  =  { every point X such that
    distance(X, Pi)  ≤  distance(X, Pj)  for every other seed Pj }

Brittle vs ductile: why metal bends but glass doesn't

Materials fail in two broad ways. Brittle materials — glass, ceramic, cast iron, ice — have almost no ability to deform permanently before breaking; stress builds up until a crack suddenly propagates through the material at high speed, often shattering it into many pieces with very little warning. Ductile materials — most metals, especially at room temperature — can stretch, bend and deform permanently (plastic deformation) before finally breaking, which is why a dented metal can survives an impact that would shatter a glass jar outright, absorbing energy through deformation rather than through crack propagation alone.

What actually decides where a crack starts

Cracks in brittle materials almost always start at existing microscopic flaws — surface scratches, trapped air bubbles, grain boundaries — because stress concentrates dramatically at any sharp geometric discontinuity, a principle engineers call stress concentration. A material can be far weaker at a scratch than the bulk material would suggest, because the scratch's sharp tip multiplies the local stress far above the average stress across the whole piece. This is precisely why a glass cutter works by scoring a shallow scratch rather than trying to cut all the way through — the scratch creates a stress concentration point where a clean crack will preferentially propagate when the glass is gently flexed.

Impact point sets the fracture pattern

Simulating a fracture usually starts by placing Voronoi seed points more densely near the impact location and more sparsely farther away, which produces the familiar real-world pattern: many small, tightly packed fragments near where the object was struck, and progressively larger fragments radiating outward. This mirrors how real impact energy actually distributes — highest stress, and therefore the most crack branching, concentrates near the point of impact, while stress (and crack density) falls off with distance.

Different materials, different cell shapes

Tuning the Voronoi cell count, size variation and randomness lets a single algorithm mimic very different real materials: glass favours many small, irregular, sharp-edged fragments; concrete favours fewer, chunkier, more angular pieces reflecting its coarser internal aggregate structure; wood fractures preferentially along its grain direction, so a realistic simulation stretches the Voronoi cells along one axis rather than keeping them isotropic; ice tends to split into long, thin shards along natural crystal planes. None of these require different physics engines — just different statistical parameters feeding the same underlying Voronoi partitioning idea.

Frequently asked questions

Why does a Voronoi diagram look like a real crack pattern?

Because both are governed by the same underlying idea: dividing a surface or material into regions around competing stress centres, where each region boundary sits at the natural equilibrium point between two neighbouring centres. Voronoi diagrams model this geometric relationship directly, which is why they visually resemble the crack networks seen in shattered glass or dried mud.

Why do metals bend instead of shattering like glass?

Metals are typically ductile: their internal atomic structure allows layers of atoms to slide past each other under stress (plastic deformation) before the material finally fails, absorbing a lot of impact energy as permanent bending rather than releasing it suddenly as crack propagation. Brittle materials like glass lack this sliding mechanism, so stress has nowhere to go except into a fast-propagating crack.

Why does scratching glass make it easier to break?

A scratch creates a sharp geometric discontinuity that concentrates stress far above the surrounding average when the glass is flexed — a principle called stress concentration. This is exactly why glass cutters work: the shallow scratch becomes the preferred starting point for a clean crack to propagate through the material.

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Voronoi Fracture: How Glass and Ice Really Break