Wrinkling reveals a new isometry of pressurized elastic shells

TL;DR

This paper investigates the post-wrinkling behavior of pressurized elastic shells under indentation, revealing a universal shape characterized by a novel isometry enabled by wrinkling in specific asymptotic limits.

Contribution

It introduces the concept of an asymptotic isometry for wrinkled shells, extending understanding beyond the initial buckling to a new universal shape in specific limits.

Findings

Wrinkling leads to a new universal shape of pressurized shells.

The asymptotic isometry emerges in the limit of weak pressure and thin shells.

This shape differs from the classical mirror-buckled form.

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.