A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of , is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of the Ghiyathiyya Madrasa in Khargird, Iran (built 1438–1444 AD). Each unit of the metamaterial consists of eight pairs of pin-jointed Y-shaped rigid elements, whereby every pair of Y-elements is elastically restrained by a spiral spring. Upon intermediate stretching, each metamaterial unit resembles the north dome of Jameh Mosque, Iran (built 1087–1088 AD), until the attainment of the fully opened configuration, which resembles a structure in Agra, India, near the Taj Mahal. Both infinitesimal and finite deformation models of the effective Young’s modulus for the metamaterial structure were established using strain energy approach in terms of the spiral spring stiffness and geometrical parameters, with assumptions to preserve the eight-fold symmetricity of every metamaterial unit. Results indicate that the prescription of strain raises the effective Young’s modulus in an exponential manner until full extension is attained. This metamaterial is useful for applications where the overall shape of the structure must be conserved in spite of uniaxial application of load, and where deformation is permitted under limited range, which is quickly arrested as the deformation progresses.

中文翻译：

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一种基于相互连接的Y元素的辅助系统，该元素受伊斯兰几何图案的启发

本文借鉴了由八个正方形的圆周排列形成的伊斯兰恒星（例如在Khargird的Ghiyathiyya Madrasa外部发现的一个伊斯兰恒星）的启发，提出了一种表现出完美的膨胀行为（即泊松比为）的2D机械超材料。伊朗（建于1438年至1444年）。超材料的每个单元由八对销钉连接的Y形刚性元件组成，其中每对Y元件都受到螺旋弹簧的弹性约束。经过中间拉伸后，每个超材料单元都类似于伊朗的贾梅清真寺的北穹顶（建于1087年至1088年），直到达到完全开放的构型为止，该构型类似于印度泰姬陵附近阿格拉的结构。利用应变能方法，根据螺旋弹簧刚度和几何参数，建立了超材料结构的有效杨氏模量的无穷小和有限变形模型，并假设保留每个超材料单元的八重对称性。结果表明，应变处方以指数方式提高了有效杨氏模量，直到达到完全伸长为止。这种超材料可用于以下应用场合：尽管单轴施加载荷，仍必须保持结构的整体形状，并且允许变形在有限的范围内，但随着变形的进行，这种变形很快会被阻止。假设保留每个超材料单元的八重对称性。结果表明，应变处方以指数方式提高了有效杨氏模量，直到达到完全伸长为止。这种超材料可用于以下应用场合：尽管单轴施加载荷，仍必须保持结构的整体形状，并且允许变形在有限的范围内，但随着变形的进行，这种变形很快会被阻止。假设保留每个超材料单元的八重对称性。结果表明，应变处方以指数方式提高了有效杨氏模量，直到达到完全伸长为止。这种超材料可用于以下应用场合：尽管单轴施加载荷，仍必须保持结构的整体形状，并且允许变形在有限的范围内，但随着变形的进行，这种变形很快会被阻止。