用于对称性保持均匀化和各向同性超材料的周期性菱形胞元
Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials
AI总结：
本文证明基于面心立方晶格的菱形胞元排列可保持组分对称性，从而利用球形夹杂物实现有效的各向同性复合材料，为周期性有序结构实现各向同性提供了理论依据。
摘要：
在基于子单元周期性排列的复合材料设计与分析中，控制与弹性响应相关的涌现材料对称性至关重要。目标材料对称性在增材制造中也扮演重要角色。在许多应用中，获得有效的各向同性材料将非常有用。虽然这些材料通常由随机微结构产生，但如何通过周期性有序结构实现各向同性尚不明确。我们证明了基于生成面心立方晶格的菱形胞元的夹杂物排列确实能保持组分的任何材料对称性，因此各向同性材料中的球形夹杂物在各向同性基体中可产生有效的各向同性复合材料。
英文摘要：
In the design and analysis of composite materials based on periodic arrangements of sub-units it is of paramount importance to control the emergent material symmetry in relation to the elastic response. The target material symmetry plays also an important role in additive manufacturing. In numerous applications it would be useful to obtain effectively isotropic materials. While these typically emerge from a random microstructure, it is not obvious how to achieve isotropy with a periodic order. We prove that arrangements of inclusions based on a rhomboidal cell that generates the Face-Centered Cubic lattice do in fact preserve any material symmetry of the constituents, so that spherical inclusions of isotropic materials in an isotropic matrix produce effectively isotropic composites.
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