Exact solutions for the wrinkle patterns of confined elastic shells
Exact solutions for the wrinkle patterns of confined elastic shells
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DOI：
10.1038/s41567-022-01672-2
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发表时间：
2020-04
期刊：
影响因子：
19.6
通讯作者：
Ian Tobasco;Yousra Timounay;D. Todorova;Graham C. Leggat;Joseph D. Paulsen;E. Katifori
中科院分区：
文献类型：
--
作者：
Ian Tobasco;Yousra Timounay;D. Todorova;Graham C. Leggat;Joseph D. Paulsen;E. Katifori
复杂的纹理表面存在于自然界和工业中，从指纹到基于平版印刷的微图案。通过限制到不相容的基底上的褶皱是产生可重构图案化形貌的有吸引力的方式，但是控制所产生的通常不对称且明显随机的褶皱仍然是一个难以捉摸的目标。在这里，我们描述了一种新的方法来了解皱纹的限制弹性壳，使用拉格朗日乘子的地方的应力。我们的理论揭示了一组简单的几何规则预测有序皱纹的出现和布局，并解释了令人惊讶的通用共存的有序和无序的皱纹域。结果与模拟和实验中的许多测试案例一致，并代表了用于设计复杂皱纹图案的基本几何工具包。
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies, but controlling the often asymmetric and apparently stochastic wrinkles that result remains an elusive goal. Here, we describe a new approach to understanding the wrinkles of confined elastic shells, using a Lagrange multiplier in place of stress. Our theory reveals a simple set of geometric rules predicting the emergence and layout of orderly wrinkles, and explaining a surprisingly generic co-existence of ordered and disordered wrinkle domains. The results agree with numerous test cases across simulation and experiment and represent an elementary geometric toolkit for designing complex wrinkle patterns.