Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the computational modeling of metastructures at macroscopic scales. In the present work, we assess the continuum limit of mechanical metamaterials via homogenized models derived rigorously from variational methods. It is shown through multiple examples that micropolar-type effective energies, derived naturally from analysis, properly capture the kinematics of discrete lattices in two and three dimensions. Moreover, the convergence of the discrete energy to the continuum limit is shown numerically. We provide open-source computational implementations for all examples, including both discrete and homogenized models.

中文翻译：

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机械超材料的均质模型


由于晶格和宏观结构尺寸之间的尺度分离，机械超材料的直接数值模拟成本高得令人望而却步。因此，多尺度连续体分析在宏观尺度上超结构的计算建模中起着关键作用。在本工作中，我们通过严格从变分方法推导出的均质模型来评估机械超材料的连续极限。通过多个示例表明，从分析中自然得出的微极型有效能量在二维和三维中正确捕获了离散晶格的运动学。此外，离散能量到连续体极限的收敛性以数字形式显示。我们为所有示例提供开源计算实现，包括离散模型和同质化模型。