Let's deflate that beach ball

TL;DR

This study explores the deflation behavior of isotropic shells, examining the relationship between pre- and post-buckling states across various thicknesses, and finds that thin shell assumptions hold up even for relatively thick shells.

Contribution

It provides experimental evidence that thin shell theory accurately describes shell behavior up to a thickness of 0.3 times the radius, using a novel low-cost measurement setup.

Findings

Shell behavior aligns with thin shell predictions before and after buckling.

The experimental setup measures volume and pressure simultaneously during deflation.

Shells up to 0.3 radius thickness still follow thin shell assumptions.

Abstract

We investigate the relationship between pre-buckling and post-buckling states as a function of shell properties, within the deflation process of shells of an isotropic material. With an original and low-cost set-up that allows to measure simultaneously volume and pressure, elastic shells whose relative thicknesses span on a broad range are deflated until they buckle. We characterize the post-buckling state in the pressure-volume diagram, but also the relaxation toward this state. The main result is that before as well as after the buckling, the shells behave in a way compatible with predictions generated through thin shell assumption, and that this consistency persists for shells where the thickness reaches up to 0.3 the shell's midsurface radius.