Davidovitch B, Schroll R D, Cerda E
Physics Department, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066115. doi: 10.1103/PhysRevE.85.066115. Epub 2012 Jun 13.
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.
已知当施加的应力超过其屈曲阈值时，薄膜的褶皱几何形状会有明显变化。在此，我们推导并分析了一组最小的、非微扰的方程，该方程描述了在最简单的轴对称几何形状中，径向褶皱从阈值到远离阈值极限（此时压缩应力消失）的连续演化过程。这种对褶皱生长的描述不同于传统的后屈曲方法，预计对高柔韧性薄片有效。我们模型的数值分析预测了两个惊人的结果。首先，褶皱数量与薄片厚度和施加的载荷呈反常比例关系，这明显与先前的预测相矛盾。其次，存在一个不变量，它表征了从阈值到远离阈值状态下褶皱幅度和数量的相互变化。
