Transition to stress focusing for a thin elastic sheet locally curved

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 for the limit of small thicknesses. Additionally, a spring network model is solved to explore the thick sheets limit and to validate the scaling behaviour of the transition for the thin sheets limit. The numerical results reveal that buckling does not exist for the thickest sheets and a stability criteria is established for the buckling of a curved sheet.