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Surface effect on the wrinkling of an elastic sheet under tension

Wrinkling of stretched elastic sheets is widely observed, and the scaling relations between the amplitude and wavelength of the wrinkles have been proposed by Cerda and Mahadevan. However, the surface effects should be taken into account when the sheet is even thinner. The surface energy was considered in this work, and the discrepancies with the classical theory has been discussed. A dimensionless parameter has been proposed to represent the size-dependence. A method of characterizing mechanical properties of thin film using wrinkles considering surface effects has also been proposed.