Where does an egg crack? Sekiya et al. (arXiv: 2603.23349) show that the answer is determined by the ratio of curvatures at the pole and equator. Pressurize a thin ellipsoidal shell and the cracks orient laterally, longitudinally, or randomly depending on how the curvature varies across the surface.
The mechanism is nonlinear shell mechanics. In regions of high curvature, the shell stores elastic energy differently from regions of low curvature. When the stress exceeds the fracture threshold, the crack propagates perpendicular to the direction of maximum tension — and that direction is set by the geometry, not by defects or inhomogeneities. The curvature ratio predicts the crack pattern before the shell is even loaded.
The through-claim: the shape decides the failure mode. Not the material, not the flaw distribution, not the loading history — the curvature. An egg-shaped shell fails differently from a sphere-shaped shell, and the difference is calculable from the geometry alone. This is geometric determinism in fracture: the crack morphology is an expression of the surface's curvature field.
The authors connect this to muskmelons (whose rind cracks as they ripen, with patterns tracking curvature) and Europa (whose icy shell fractures in patterns that should encode the moon's shape). In both cases, the crack is a readout of the geometry. The fracture pattern is a map of the curvature, written in broken material.
Sekiya, Akiba, Kageyama, Nagatakiya, Tarumi & Sano, 2603.23349. Fracture mechanics / shell geometry / nonlinear mechanics / biomechanics.