Geometry and Physics of Wrinkling
E. Cerda1,2 and L. Mahadevan1 *
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom
2Departamento de Física, Universidad de Santiago de Chile, Avenida Ecuador 3493, Casilla 307, Correo 2, Santiago, Chile
Received 25 June 2002; published 19 February 2003
The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the instability, using elementary geometry and the physics of bending and stretching. Our main result is a set of simple scaling laws; the wavelength of the wrinkles λ^K-1/4, where K is the stiffness due to an oeelastic substrate” effect with a multitude of origins, and the amplitude of the wrinkle A^λ. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.