Sequential buckling in fluid-filled cylindrical shells.

From oil drums to flying rockets, cylindrical shells are valued for their load-carrying capacity. When sufficiently compressed, they buckle, with the phenomenon taking many forms, from periodic diamond-shaped buckles to localized elephant footing. The precise physical mechanisms of buckling are different, for example, in empty shells and shells with a solid core. However, despite the abundance of liquid-filled shells in industry and everyday life, their buckling is largely overlooked. Here, we compress beverage cans and identify a sequential buckling instability that localizes circumferential rings above a critical level of compression. Combining measurements of the anisotropic material properties of the shell with modelling based on the nonlinear Swift-Hohenberg equations, we demonstrate that fluid-filled shells can support a multiplicity of localized solutions, which are induced by the nonlinear hoop stress of the shell and sequentialize through homoclinic snaking. This establishes a rare link between idealized mathematical studies of pattern formation and physical realizations of spatially-localized buckling phenomena. These findings serve as a blueprint for exploring localized patterns induced by material nonlinearities, near-incompressibility and pressurization in other physical systems.