Transition to stress focusing for locally curved sheets

TL;DR

This paper investigates the transition to stress focusing and buckling in thin elastic sheets with local curvature, identifying a critical width for buckling and validating scaling laws through experiments and models.

Contribution

It introduces a new understanding of buckling transition in curved sheets, combining experimental observations with a spring network model to explore different thickness regimes.

Findings

Buckling with stress focusing occurs when sheet width exceeds a critical value proportional to sheet length.

A scaling law with an exponent of 2/3 describes the transition in thin sheets.

Buckling does not occur in the thickest sheets, and a stability criterion is established.

Abstract

A rectangular thin elastic sheet is deformed by forcing a contact between two points at the middle of its length. A transition to buckling with stress focusing is reported for the sheets sufficiently narrow with a critical width proportional to the sheet length with an exponent 2/3 in the small thickness limit. Additionally, a spring network model is solved to explore the thick sheet limit and to validate the scaling behaviour of the transition in the thin sheet limit. The numerical results reveal that buckling does not exist for the thickest sheets and a stability criterion is established for the buckling of a curved sheet.