Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

TL;DR

This study numerically explores how elastic spherical shells deform under volume reduction, revealing buckling behaviors, the influence of Poisson's ratio, and providing insights into shell features from observed shapes.

Contribution

It offers a detailed numerical analysis of buckling modes in elastic shells, highlighting the role of Poisson's ratio and unifying deformation curves, which advances understanding of shell stability.

Findings

First buckling occurs via axisymmetric dimple formation.

Second buckling involves folding and loss of axisymmetry.

Poisson's ratio significantly influences buckling behavior.

Abstract

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such surface may modelize a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It first occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry, by folding along portions of meridians. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of the Poisson's ratio. After the second buckling, the number of folds and inner pressure are investigated, allowing to infer shell features from mere observation and/or knowledge of external constraints.