  In this work, we consider the stability of a spherical shell under combined
loading from a uniform external pressure and a homogenous natural curvature.
Non-mechanical stimuli, such as one that tends to modify the rest curvature of
an elastic body, are prevalent in a wide range of natural and engineered
systems, and may occur due to thermal expansion, changes in pH, differential
swelling, and differential growth. Here, we investigate how the presence of
both an evolving natural curvature and an external pressure modifies the
stability of a complete spherical shell. We show that due to a mechanical
analogy between pressure and curvature, positive natural curvatures can
severely destabilize a thin shell, while negative natural curvatures can
strengthen the shell against buckling, providing the possibility to design
shells that buckle at or above the theoretical limit for pressure alone, i.e. a
knock-up factor. These results extend directly from the classical analysis of
the stability of shells under pressure, and highlight the important role that
non-mechanical stimuli can have on modifying the the membrane state of stress
in a thin shell.
