Regimes of wrinkling in pressurized elastic shells

TL;DR

This paper analyzes the wrinkling behavior of pressurized elastic shells under indentation, combining analytical and simulation methods to understand wrinkle patterns and their dependence on pressure and indentation depth.

Contribution

It provides a detailed 'Far from threshold' analysis of wrinkling in pressurized shells, extending beyond standard stability approaches.

Findings

Number of wrinkles increases with pressurization at instability onset

Wrinkle patterns evolve spatially with indentation depth

Quantitative differences identified between 'Far from threshold' and 'Near threshold' analyses

Abstract

We consider the point-indentation of a pressurized elastic shell. It has previously been shown that such a shell is subject to a wrinkling instability as the indentation depth is quasi-statically increased. Here we present detailed analysis of this wrinkling instability using a combination of analytical techniques and finite element simulations. In particular, we study how the number of wrinkles observed at the onset of instability grows with increasing pressurization. We also study how, for fixed pressurization, the number of wrinkles changes both spatially and with increasing indentation depth beyond onset. This `Far from threshold' analysis exploits the largeness of the wrinkle wavenumber that is observed at high pressurization and leads to quantitative differences with the standard `Near threshold' stability analysis.