Wrinkling reveals a new isometry of pressurized elastic shells

Abstract

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.

6 pages main text plus 14 pages of supplementary information

References in corpus (4)

• Indentation of ultrathin elastic films and the emergence of asymptotic isometry
• A sheet on deformable sphere: "wrinklogami" patterns suppress curvature-induced delamination
• The secondary buckling transition: wrinkling of buckled spherical shells
• Secondary polygonal instability of buckled spherical shells

Cited by in corpus (12)

• Indentation metrology of clamped, ultra-thin elastic sheets
• Wrapping liquids, solids, and gases in thin sheets
• Regimes of wrinkling in pressurized elastic shells
• The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling'
• Partial wetting of thin solid sheets under tension
• Regimes of wrinkling in an indented floating elastic sheet
• From cylindrical to stretching ridges and wrinkles in twisted ribbons
• Indentation of a floating elastic sheet: Geometry versus applied tension
• Wrinkling of a thin circular sheet bonded to a spherical substrate
• Crumples as a generic stress-focusing instability in confined sheets
• Geometry underlies the mechanical stiffening and softening of an indented floating film
• A unified geometric framework for axisymmetric thin sheet buckling