Regimes of wrinkling in pressurized elastic shells

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 375; no. 2093; p. 20160330
• Main Authors: Taffetani, Matteo, Vella, Dominic
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 13.05.2017
• Subjects: Complex media; Elastic shells; Far From Threshold Wrinkling; Finite element method; Finite-Element Analysis; Indentation; Pressurization; Shallow Shell Theory; Shell stability; Stability analysis; Wavelengths; Wrinkling; shallow shell theory; Far from threshold wrinkling; finite-element analysis
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2016.0330

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. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’