Cerda E, Mahadevan L
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
Phys Rev Lett. 2003 Feb 21;90(7):074302. doi: 10.1103/PhysRevLett.90.074302. Epub 2003 Feb 19.
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.
薄弹性片的起皱现象出现在一系列长度尺度范围内，从细胞爬行的基质上的精细尺度图案到衣服上可见的粗大皱纹。受拉伸弹性片起皱现象的启发，我们运用基本几何原理以及弯曲和拉伸物理学，推导出了一种远离不稳定性起始点时有效的起皱通用理论。我们的主要成果是一组简单的标度律；皱纹波长λ近似为K^(-1/4)，其中K是由于多种来源的“弹性基底”效应产生的刚度，皱纹幅度A近似为λ。这些标度律可为用于薄固体膜力学特性表征的高灵敏度定量起皱分析提供基础。
