Nonperturbative model for wrinkling in highly bendable sheets
Nonperturbative model for wrinkling in highly bendable sheets
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DOI：
10.1103/physreve.85.066115
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发表时间：
2012-06-13
影响因子：
2.4
通讯作者：
Cerda, E.
中科院分区：
文献类型：
--
作者：
Davidovitch, B.;Schroll, R. D.;Cerda, E.
薄膜的褶皱几何形状是众所周知的变化明显的，因为施加的应力超过其屈曲阈值。在这里，我们推导和分析一个最小的，非微扰的方程组，捕捉最简单的轴对称几何形状的径向皱纹的连续演变从阈值到远离阈值的限制，压缩应力崩溃。这种描述的皱纹的增长是不同于传统的后屈曲的方法，预计是有效的高度可弯曲的板。我们的模型的数值分析预测了两个令人惊讶的结果。首先，褶皱的数量与片材的厚度和施加的载荷成比例，这与先前的预测明显矛盾。第二，存在一个不变量，其特征在于从阈值到远离阈值的制度的皱纹的幅度和数量的相互变化。
The wrinkled geometry of thin films is known to vary appreciably as the applied stresses exceed their buckling threshold. Here we derive and analyze a minimal, nonperturbative set of equations that captures the continuous evolution of radial wrinkles in the simplest axisymmetric geometry from threshold to the far-from-threshold limit, where the compressive stress collapses. This description of the growth of wrinkles is different from the traditional post-buckling approach and is expected to be valid for highly bendable sheets. Numerical analysis of our model predicts two surprising results. First, the number of wrinkles scales anomalously with the thickness of the sheet and the exerted load, in apparent contradiction with previous predictions. Second, there exists an invariant quantity that characterizes the mutual variation of the amplitude and number of wrinkles from threshold to the far-from-threshold regime.