Buckling pathways in spherical shells with soft spots

Thin elastic spherical shells are known to exhibit a buckling instability at a finite external pressure. We study how this buckling is influenced by a weak region in an otherwise uniform shell, focusing on the case of a single small circular soft spot that is thinner than the rest of the shell. Using numerical simulations and theoretical arguments, we show that the soft region fundamentally alters the buckling behavior of the shell. The soft spot influences both the pressure at which the shell buckles, and the postbuckling shape of the shell. Depending on the properties of the soft spot, we find either a single buckling transition or two separate transitions as the external pressure is increased. We analyze the dependence of these buckling transitions on the size and thickness of the soft region. Besides contributing to our fundamental understanding of buckling transitions in inhomogeneous shells, our results can be applied to designing capsules with tunable shapes.