In this paper, we extend the discrete-to-continuum procedure we developed in Español et al. (2018) to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing elastic terms and a weak interaction term that could utilize either a Lennard-Jones potential or a Kolmogorov–Crespi potential. To validate our modeling, we perform numerical simulations to compare the predictions of the original discrete model and the proposed continuum model, which also show an agreement with experimental findings for, e.g., twisted bilayer graphene.

中文翻译：

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弱相互作用的不相称二维晶格的离散到连续模型：六角形情况

在本文中，我们扩展了我们在 Español 等人中开发的离散到连续过程。(2018) 推导出六角形扭曲双层材料的连续变分模型，其中一层是固定的。我们使用包含弹性项的离散能量和可以利用 Lennard-Jones 势或 Kolmogorov-Crespi 势的弱相互作用项。为了验证我们的模型，我们进行了数值模拟来比较原始离散模型和建议的连续模型的预测，这也表明与实验结果一致，例如，扭曲的双层石墨烯。