A controlled surface wrinkling pattern has been widely used in diverse applications such as stretchable electronics, smart windows, and haptics. Here, we focus on hexagonal wrinkling patterns because of their great potentials in realizing anisotropic and tunable friction and serving as a dynamical template for making non-flat thin films through self-assembling processes. We employ large-scale finite element simulations of a bilayer neo-Hookean solid (e.g., a film bonded on a substrate) to explore mechanical principles that govern the formation of hexagonal wrinkling patterns and strategies for making nearly perfect hexagonal patterns. In our model, the wrinkling instabilities are driven by the confined film expansion. Our results indicate robust hexagonal patterns exist at a relatively small modulus mismatch (on the order of 10) between the film and substrate. Besides, the film expansion should not exceed the onset of wrinkling value too much to avoid post-buckling patterns. By harnessing the imperfection insensitivity of one dimension sinusoidal wrinkles, we apply a sequential loading to the bilayer structure to produce the nearly perfect hexagonal patterns. Lastly, we discuss the connection between the simple bilayer model and the gradient structures commonly existed in experiments.

中文翻译：

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理解和控制新胡克弹性双层结构中皱纹的六边形图案

受控的表面起皱图案已广泛用于各种应用，例如可拉伸电子产品、智能窗户和触觉。在这里，我们专注于六边形褶皱图案，因为它们在实现各向异性和可调摩擦以及作为通过自组装过程制造非平面薄膜的动态模板方面具有巨大潜力。我们对双层新胡克固体（例如，粘合在基材上的薄膜）进行大规模有限元模拟，以探索控制六边形褶皱图案形成的机械原理以及制作近乎完美的六边形图案的策略。在我们的模型中，起皱不稳定性是由受限膜膨胀驱动的。我们的结果表明稳健的六边形图案存在于薄膜和基材之间相对较小的模量失配（大约 10）。此外，薄膜膨胀不应超过起皱值太多以避免后屈曲图案。通过利用一维正弦皱纹的缺陷不敏感性，我们对双层结构应用顺序加载以产生近乎完美的六边形图案。最后，我们讨论了简单双层模型与实验中普遍存在的梯度结构之间的联系。我们对双层结构应用顺序加载以产生近乎完美的六边形图案。最后，我们讨论了简单双层模型与实验中普遍存在的梯度结构之间的联系。我们对双层结构应用顺序加载以产生近乎完美的六边形图案。最后，我们讨论了简单双层模型与实验中普遍存在的梯度结构之间的联系。