Volume 112, Number 2, October 2015
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||16 November 2015|
Wrinkling reveals a new isometry of pressurized elastic shells
1 Mathematical Institute, University of Oxford - Woodstock Rd, Oxford, OX2 6GG, UK
2 Department of Mechanical and Industrial Engineering, Northeastern University - Boston, MA 02115, USA
3 Physics Department, University of Massachusetts - Amherst, MA 01003, USA
Received: 26 August 2015
Accepted: 21 October 2015
We consider the point indentation of a pressurized, spherical elastic shell. Previously it was shown that such shells wrinkle once the indentation reaches a threshold value. Here, we study the behaviour of this system beyond the onset of instability. We show that rather than simply approaching the classical “mirror-buckled” shape, the wrinkled shell approaches a new, universal shape that reflects a nontrivial type of isometry. For a given indentation depth, this “asymptotic isometry”, which is only made possible by wrinkling, is reached in the doubly asymptotic limit of weak pressure and vanishing shell thickness.
PACS: 46.32.+x – Static buckling and instability / 46.70.De – Beams, plates, and shells / 62.20.D- – Elasticity
© EPLA, 2015
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