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

TL;DR

This paper uses elasticity theory to predict the number of depressions on a spherical shell's surface under external pressure, showing how it varies with volume change and aligning with experimental data.

Contribution

It introduces a model that predicts depression count based on volume variation, emphasizing curvature effects and steric constraints.

Findings

Number of depressions depends on volume variation

N increases up to 6 then decreases with larger volume changes

Predictions align with experimental observations

Abstract

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. In a model that mainly considers curvature deformations, we show that N only depends on the relative volume variation. Equilibrium configurations show single depression (N=1) for small volume variations, then N increases up to 6, before decreasing more abruptly due to steric constraints, down to N=1 again for maximal volume variations. These predictions are consistent with previously published experimental observations.