Fracture networks span scales from millimeter cracks in botanical peels to hundred-kilometer lineae on planetary satellites. A unified framework explaining how surface geometry prescribes fracture morphology has been missing.
Researchers internally pressurized thin bilayer spheroidal shells and demonstrated that shell curvature provides a geometric blueprint for fracture. The crack morphology โ lateral, longitudinal, or random โ depends on the curvature ratio between the pole and the equator. The diversity of patterns arises from nonlinear shell mechanics: the curvature determines stress anisotropy, which determines where and how cracks propagate.
The framework integrates nonlinear geometry with classical Griffith fracture criteria and von Mises yield criteria. The curvature ratio predicts crack orientation before the crack forms. The geometry precedes the fracture.
The validation is cross-scale: ripening muskmelons and the icy crust of Europa follow the same geometric principles as the laboratory shells. A melon's surface cracks and a moon's tectonic lineae share the same curvature-to-fracture mapping. The materials are different (biological tissue vs. ice vs. polymer bilayer). The physics is the same (stress anisotropy from curved geometry).
The through-claim: when fracture patterns seem to require material-specific explanations, check the geometry first. Curvature prescribes stress, stress prescribes fracture, and curvature is a property of shape, not substance. The crack pattern was written into the surface before the material was chosen.