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.

超材料表现出与常规弹性不同的材料响应偏差。由于扩展了理论而以引入附加参数为代价，这种现象被广义弹性所捕获。这些参数链接到内部长度刻度。在宏观水平上描述，具有微观长度尺度上的子结构的材料要求引入附加的本构参数。因此，原则上，在对子结构有准确知识的情况下，渐近均匀化对于确定这些参数是可行的。尤其是在填充率已知的增材制造中，拓扑优化会引入一个子结构，从而导致机械响应中的高阶项。因此，减轻重量可创建具有精确已知子结构的超材料。在这里 我们开发了一种使用两种比例尺来数字识别超材料参数的计算方案。作为一个具体示例，我们将其应用于蜂窝子结构并讨论填充率。这种计算方法适用于广泛的子结构并利用开源代码。我们将其公开提供以进行透明的科学交流。