论文标题
严格弹性壳的皱纹模式的确切解决方案
Exact solutions for the wrinkle patterns of confined elastic shells
论文作者
论文摘要
复杂的纹理表面发生在自然和工业中，从指纹到基于光刻的微图案。通过将不兼容的底物限制来皱纹是产生可重新配置图案的地形图的一种有吸引力的方式，但是控制经常不对称且显然是随机皱纹的皱纹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，可以使用拉格朗日乘法器代替压力来理解受限弹性壳的皱纹。我们的理论揭示了一组简单的几何规则，可以预测有序皱纹的出现和布局，并解释了有序和混乱的皱纹域的令人惊讶的通用共存。结果与模拟和实验中的许多测试用例一致，并代表用于设计复杂皱纹模式的基本几何工具包。
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.
