  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.
