Fish Cells as a new metamaterial with zero Poisson’s ratio in two planar directions is introduced with application in morphing aircraft skin. In order to tailor the design of this metamaterial for arbitrary loadings, equivalent elastic properties of the Fish Cells metamaterial are derived and analyzed using analytical and numerical methods. The admissible range of geometric parameters is presented and variation of elastic properties with parameters is studied. The effective elastic modulus of the metamaterial is derived analytically and verified with finite element models. The in-plane and transverse shear modulus of the metamaterial are evaluated using finite element analysis where accurate periodic boundary conditions for in-plane shear loading are investigated. The lower and upper bounds of the transverse shear modulus are derived based on strain and complementary energy relations which are verified with finite element results. As zero Poisson’s ratio behavior of the Fish Cells topology is proved, derivative geometries from this topology with zero Poisson’s ratio behavior are also presented.

中文翻译：

---

鱼细胞，一种新的零泊松比超材料——第二部分：弹性特性

鱼细胞作为一种在两个平面方向上具有零泊松比的新型超材料被引入并应用于飞机蒙皮变形。为了针对任意载荷定制这种超材料的设计，使用解析和数值方法导出和分析了鱼细胞超材料的等效弹性特性。给出了几何参数的允许范围，研究了弹性性能随参数的变化规律。超材料的有效弹性模量是通过分析导出的，并用有限元模型进行验证。使用有限元分析来评估超材料的平面内和横向剪切模量，其中研究了平面内剪切载荷的精确周期性边界条件。横向剪切模量的下限和上限是基于应变和互补能量关系推导出来的，这些关系用有限元结果进行了验证。由于证明了 Fish Cells 拓扑的零泊松比行为，因此还提供了来自该拓扑的具有零泊松比行为的导数几何。