Geometry and physics of wrinkling.
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 lambda approximately K(-1/4), where K is the stiffness due to an "elastic substrate" effect with a multitude of origins, and the amplitude of the wrinkle A approximately lambda. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.
Cerda
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Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
Mahadevan
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D004548:Elasticity; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D020959:Polyethylene / Q000737:chemistry; D015595:Skin Aging; D013718:Tensile Strength
D020959:Polyethylene