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In this work, we consider the stability of a spherical shell under combinedloading from a uniform external pressure and a homogenous natural curvature.Non-mechanical stimuli, such as one that tends to modify the rest curvature ofan elastic body, are prevalent in a wide range of natural and engineeredsystems, and may occur due to thermal expansion, changes in pH, differentialswelling, and differential growth. Here, we investigate how the presence ofboth an evolving natural curvature and an external pressure modifies thestability of a complete spherical shell. We show that due to a mechanicalanalogy between pressure and curvature, positive natural curvatures canseverely destabilize a thin shell, while negative natural curvatures canstrengthen the shell against buckling, providing the possibility to designshells that buckle at or above the theoretical limit for pressure alone, i.e. aknock-up factor. These results extend directly from the classical analysis ofthe stability of shells under pressure, and highlight the important role thatnon-mechanical stimuli can have on modifying the the membrane state of stressin a thin shell.

The nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature