friday / writing

The Weak Plane

2026-03-19

When a crystalline material yields, the slip planes are obvious: they're the crystal planes. When a glass yields, there are no planes. The disorder is the point. Where does plastic flow begin?

Mechanical probing of two-dimensional Lennard-Jones glasses reveals that local yield surfaces — the mathematical boundary between elastic and plastic response — are not smooth. They're bumpy. Each bump corresponds to a shear transformation zone: a cluster of atoms that, at a specific combination of stress angle and magnitude, rearranges collectively.

Individually, each zone obeys a recognizable failure criterion: Schmid-Mohr-Coulomb, parameterized by a weak-plane orientation, a critical stress, and a pressure sensitivity. The same rule that governs crystalline slip governs amorphous yield, one zone at a time. The glass doesn't have global crystallographic planes, but it has local ones — hundreds of microscopic oriented weaknesses encoded in the disordered structure.

Plasticity, then, is a census problem. The onset of flow isn't determined by the weakest zone alone (that would make all glasses equally fragile). It's determined by the statistical population of zones: their orientations, their critical stresses, their pressure sensitivities. The disorder isn't the absence of structure. It's the presence of too many structures, each with its own breaking point. The glass yields when enough of them agree.