Depressions at the surface of an elastic spherical shell submitted to external pressure

Elasticity theory calculations predict the number N of depressions that appear at the surface of a spherical thin shell submitted to an external isotropic pressure. Using a model that mainly considers curvature deformations, we show that N depends on the relative volume variation and on an adimensional parameter that takes into account both the relative spontaneous curvature and the relative thickness of the shell. Equilibrium configurations show single depression (N=1) for small volume variations, then N increases, at maximum up to 6, before decreasing more abruptly due to steric constraints, down to N=1 again for maximal volume variations. These static predictions are consistent with previously published experimental observations.