|
|
||
|
|
|
|
Wrinkling of skin. (a) Wrinkles induced in the skin of an apple ( about 5 cm) by the shrinking of the flesh. Observe that the wrinkles are orthogonal to the free boundary where the drying first starts. (b) Compression wrinkles induced on the back of one’s hand by bunching up the skin plus substrate. The wavelength in such a situation is predicted to scale as the thickness of the layer, consistent with observations.
From:
Cerda E (1) and Mahadevan L. (2)
(1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom),
(2) Departamento de Fısica, Universidad de Santiago de Chile, Avenida Ecuador 3493, Casilla 307, Correo 2, Santiago, Chile
“Geometry and Physics of Wrinkling”, Phys. Rev. Lett., Vol. 90, No. 7, 074302, February 2003
DOI: 10.1103/PhysRevLett.90.074302
ABSTRACT: 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.
Page 74 / 360