We showed a panoptic view of architectured planar lattices based on star-polygon tilings. Four star-polygon-based lattice sub-families were investigated numerically and experimentally. Finite element-based homogenization allowed computation of Poisson's ratio, elastic modulus, shear modulus, and planar bulk modulus. A comprehensive understanding of the range of properties and micromechanical deformation mechanisms was developed. By adjusting the star angle from $0^\circ$ to the uniqueness limit ($120^\circ$ to $150^\circ$), our results showed an over 250-fold range in elastic modulus, over a 10-fold range in density, and a range of $-0.919$ to $+0.988$ for Poisson's ratio. Additively manufactured lattices showed good agreement in properties. The additive manufacturing procedure for each lattice is available on www.fullcontrol.xyz/#/models/1d3528. Three of the four sub-families exhibited in-plane elastic isotropy. One showed high stiffness with auxeticity at low density with a primarily axial deformation mode as opposed to bending deformation for the other three lattices. The range of achievable properties, demonstrated with property maps, proves the extension of the conventional material-property space. Lattice metamaterials with Triangle-Triangle, Kagome, Hexagonal, Square, Truncated Archimedean, Triangular, and Truncated Hexagonal topologies have been studied in the literature individually. We show that all these structures belong to the presented overarching lattices.

中文翻译：

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基于星形多边形瓦片的架构平面晶格的弹性静力学

我们展示了基于星形多边形拼贴的架构平面晶格的全景视图。对四个基于星形多边形的晶格亚族进行了数值和实验研究。基于有限元的均质化允许计算泊松比、弹性模量、剪切模量和平面体积模量。开发了对性能范围和微机械变形机制的全面了解。通过将星角从 $0^\circ$ 调整到唯一性限制（$120^\circ$ 到 $150^\circ$），我们的结果显示弹性模量范围超过 250 倍，密度范围超过 10 倍，泊松比的范围为 $-0.919$ 到 $+0.988$。增材制造的晶格在性能上表现出良好的一致性。每个晶格的增材制造程序可在 www.fullcontrol 上找到。xyz/#/models/1d3528. 四个亚族中的三个表现出面内弹性各向同性。一个显示出高刚度和低密度拉胀性，主要是轴向变形模式，而不是其他三个晶格的弯曲变形。用属性图展示的可实现属性的范围证明了传统材料-属性空间的扩展。具有三角形-三角形、Kagome、六边形、正方形、截断阿基米德、三角形和截断六边形拓扑的晶格超材料已在文献中单独进行了研究。我们表明，所有这些结构都属于所呈现的总体晶格。一个显示出高刚度和低密度拉胀性，主要是轴向变形模式，而不是其他三个晶格的弯曲变形。用属性图展示的可实现属性的范围证明了传统材料-属性空间的扩展。具有三角形-三角形、Kagome、六边形、正方形、截断阿基米德、三角形和截断六边形拓扑的晶格超材料已在文献中单独进行了研究。我们表明，所有这些结构都属于所呈现的总体晶格。一个显示出高刚度和低密度拉胀性，主要是轴向变形模式，而不是其他三个晶格的弯曲变形。用属性图展示的可实现属性的范围证明了传统材料-属性空间的扩展。具有三角形-三角形、Kagome、六边形、正方形、截断阿基米德、三角形和截断六边形拓扑的晶格超材料已在文献中单独进行了研究。我们表明，所有这些结构都属于所呈现的总体晶格。和截断六边形拓扑已在文献中单独进行了研究。我们表明，所有这些结构都属于所呈现的总体晶格。和截断六边形拓扑已在文献中单独进行了研究。我们表明，所有这些结构都属于所呈现的总体晶格。