Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange.

中文翻译：

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增材制造通过渐近均匀化引入了超材料参数的子结构和计算确定

超材料表现出与传统弹性的材料响应偏差。这种现象被广义弹性捕获，这是以引入额外参数为代价扩展理论的结果。这些参数与内部长度刻度相关联。在宏观水平上描述在微观长度尺度上具有子结构的材料需要引入额外的本构参数。因此，原则上，给定对子结构的准确知识，渐近均质化是可行的来确定这些参数。特别是在增材制造中，在填充率下，拓扑优化引入了导致机械响应中更高阶项的子结构。因此，重量减轻创造了一种具有准确已知子结构的超材料。在此处，我们开发了一种使用两种尺度的计算方案，用于数值识别超材料参数。作为一个具体的例子，我们将其应用于蜂窝状子结构并讨论填充率。这种计算方法适用于广泛的类子结构并利用开源代码；我们将其公开以进行透明的科学交流。