Universal wrinkling of supported elastic rings

TL;DR

This paper presents an exactly solvable model for the universal wrinkling behavior of substrate-supported elastic rings under compression, providing analytical expressions and confirming predictions with numerical results.

Contribution

It introduces a new analytical model that describes the universal wrinkling patterns of supported elastic rings, linking them to buckled unsupported states.

Findings

Analytical expressions for universal wrinkle shapes

Agreement between analytical and numerical results

Identification of pressure-tension relations at wrinkle emergence

Abstract

An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported ring and are therefore universal. Closed analytical expressions for the resulting universal shapes are provided, including the one-to-one relations between the pressure and tension at which these emerge. The analytical predictions agree with numerical continuation results to within numerical accuracy, for a large range of parameter values, up to the point of self-contact.