We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new procedure involving the concept of apparent material stiffness of a unit-cell under affine Dirichlet boundary conditions and Neumann’s principle on the overall representation of anisotropy. We explain our idea of “maximal” stiffness of the unit-cell and use state of the art first order numerical homogenization methods to obtain the needed parameters for a given tetragonal unit-cell. These results are used in the accompanying paper (d’Agostino et al. in J. Elast. 2019 . Accepted in this volume) to describe the wave propagation including band-gaps in the same tetragonal metamaterial.

中文翻译：

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通过模型适应的一阶均质化在松弛微晶模型中识别与尺度无关的材料参数

对于给定的周期性微观结构，我们严格确定松弛微晶广义连续模型中与尺度无关的短程弹性参数。这是使用经典的周期性均质化和涉及仿射狄利克雷边界条件下晶胞表观材料刚度概念和各向异性总体表示的诺依曼原理的新程序来完成的。我们解释了我们关于晶胞“最大”刚度的想法，并使用最先进的一阶数值均化方法来获得给定四方晶胞所需的参数。这些结果用于随附的论文（d'Agostino 等人，在 J. Elast. 2019 中。本卷已接受）来描述波传播，包括同一四方超材料中的带隙。