Crack propagation on bilayer spherical shells

Crack patterns are fracture histories of material and structures, across different length scales from fruits, paintings, trees, and rocks to even the planetary scales. Fracture is a complex nonlinear phenomenon coupled with material and geometric non-linearity. Although theoretical and experimental modelling have been proposed, the prediction and control of crack propagation is still challenging in structural mechanics. Here, as a model system to uncover the relation of material and geometric non-linearity in fracture phenomena, we study crack patterns on the surface of pressurized bi-layer shells. Our bi-layer shell is a thin elastic shell coated by another outer thin layer of brittle silicone elastomer. As we pressurize the shell from the inside, the shell inflates, the outer layer only fractures, and then the cracks propagate on the outer surface. This model system is inspired by the mechanisms of the mesh pattern formation of muskmelons. Based on experiments, we find that the natural curvature of the shell plays an important role in the crack propagation direction on the shell surface, indicating that the crack could be controlled by the geometry of the substrate. This geometric scenario is supplemented by the computation of the strain fields in the one-dimensional model of a pressurized elastic shell.