Owing to the fact that effective properties of low-density cellular solids heavily rely on their underlying architecture, a variety of explicit and implicit techniques exists for designing cellular geometries. However, most of these techniques fail to present a correlation among architecture, internal forces, and effective properties. This paper introduces an alternative design strategy based on the static equilibrium of forces, equilibrium of polyhedral frames, and reciprocity of form and force. This novel approach reveals a geometric relationship among the truss system architecture, topological dual, and equilibrium of forces on the basis of 3D graphic statics. This technique is adapted to devise periodic strut-based cellular architectures under certain boundary conditions and they are manipulated to construct shell-based (shellular) cells with a variety of mechanical properties. By treating the materialized unit cells as representative volume elements (RVE), multiscale homogenization is used to investigate their effective linear elastic properties. Validated by experimental tests on 3D printed funicular materials, it is shown that by manipulating the RVE topology using the proposed methodology, alternative strut materialization schemes, and rational addition of bracing struts, cellular mechanical metamaterials can be systematically architected to demonstrate properties ranging from bending- to stretching-dominated, realize metafluidic behavior, or create novel hybrid shellulars.

中文翻译：

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基于支柱的蜂窝到壳索材料

由于低密度蜂窝固体的有效特性在很大程度上依赖于它们的底层结构，因此存在用于设计蜂窝几何形状的各种显式和隐式技术。然而，这些技术中的大多数未能呈现架构、内力和有效属性之间的相关性。本文介绍了一种基于力的静态平衡、多面体框架的平衡以及形式和力的互易性的替代设计策略。这种新颖的方法在 3D 图形静力学的基础上揭示了桁架系统架构、拓扑对偶和力平衡之间的几何关系。该技术适用于在某些边界条件下设计周期性的基于支柱的细胞结构，并对其进行操作以构建具有各种机械性能的基于壳（壳）的细胞。通过将物化的晶胞作为代表体积元素 (RVE)，使用多尺度均质化来研究它们的有效线弹性特性。通过 3D 打印索道材料的实验测试验证，表明通过使用所提出的方法、替代支柱物化方案和合理添加支撑支柱来操纵 RVE 拓扑结构，可以系统地构建蜂窝机械超材料以展示从弯曲到以拉伸为主，实现元流体行为，或创造新的混合壳。