Audoly B, Boudaoud A
Laboratoire de modélisation en mécanique, UMR 7607 du CNRS, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France.
Phys Rev Lett. 2003 Aug 22;91(8):086105. doi: 10.1103/PhysRevLett.91.086105. Epub 2003 Aug 21.
We study the buckling of thin elastic plates caused by residual strains concentrated near a free edge. This is a model for plant leaves and torn plastic sheet morphologies. We derive new governing equations explaining self-similar patterns reported earlier in experiments. We reveal the cascade mechanism, determine the bounds for its wavelengths, and predict a similarity factor of 3 in agreement with experiments. This is confirmed by numerical solutions with up to five generations of wrinkles.
我们研究了由自由边缘附近集中的残余应变引起的薄弹性板的屈曲。这是植物叶子和撕裂塑料薄膜形态的一个模型。我们推导了新的控制方程，解释了早期实验中报道的自相似模式。我们揭示了级联机制，确定了其波长的界限，并预测了与实验一致的3的相似因子。这通过具有多达五代皱纹的数值解得到了证实。
