Abstract
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.
Highlights
Mechanics of metamaterials is gaining an increased interest owing to additive manufacturing technologies allowing us to craft sophisticated structures with different length scales
Substructure-related change leads to metamaterials, and this phenomenon is explained by theoretical arguments by assuming conventional elasticity in the smaller length scale leading to generalized elasticity in the larger length scale [14–18]
For example in fused deposition modeling (FDM), the filaments are made of non-porous material and the porosity is caused by design
Summary
Mechanics of metamaterials is gaining an increased interest owing to additive manufacturing technologies allowing us to craft sophisticated structures with different length scales. Material is saved by introducing a substructure. Substructure-related change in materials response is already known [1– 3], studied under different assumptions [4–9], and verified experimentally [10–13]. Substructure-related change leads to metamaterials, and this phenomenon is explained by theoretical arguments by assuming conventional elasticity in the smaller length scale (microscale) leading to generalized elasticity in the larger length scale (macroscale) [14–18].
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