具有弹性界面的手征二维周期块体材料：拉胀和声学性质
Chiral two-dimensional periodic blocky materials with elastic interfaces: auxetic and acoustic properties
摘要：
两个新的手性块晶格拓扑结构在这里设想有有趣的拉胀和声学行为。结构化手性材料由通过线性弹性界面连接的正方形或六边形刚性和重块的周期性重复组成，其手性由块相对于连接它们的质心的线的相等旋转产生。推导了拉格朗日模型的控制方程，并利用厄米特本征值问题得到了频率能带结构。等效微极连续谱通过标准连续化方法解析推导，与Bacigalupo和Gambarotta（2017）提出的程序一致，从中推导出频谱的近似值。此外，通过适当的凝聚过程，得到了等效柯西连续体的整体弹性模量的封闭形式。通过参数分析，得到了界面的总弹性模量和频率能带结构，并分析了手征角和切向刚度与法向刚度之比对界面的影响。最后，它示出了如何手征性和接口刚度可能会影响强auxeticity和如何等效微极模型提供的色散曲线在很宽的范围内的波矢量幅度与当前的非常一致。
英文摘要：
Two novel chiral block lattice topologies are here conceived having interesting auxetic and acoustic behavior. The architectured chiral material is made up of a periodic repetition of square or hexagonal rigid and heavy blocks connected by linear elastic interfaces, whose chirality results from an equal rotation of the blocks with respect to the line connecting their centroids. The governing equation of the Lagrangian model is derived and a hermitian eigenproblem is formulated to obtain the frequency band structure. An equivalent micropolar continuum is analytically derived through a standard continualization approach in agreement with the procedure proposed by Bacigalupo and Gambarotta (2017) from which an approximation of the frequency spectrum is derived. Moreover, the overall elastic moduli of the equivalent Cauchy continuum are obtained in closed form via a proper condensation procedure. The parametric analysis involving the overall elastic moduli of the Cauchy equivalent continuum model and the frequency band structure is carried out to catch the influence of the chirality angle and of the ratio between the tangential and normal stiffness of the interface. Finally, it is shown how chirality and interface stiffness may affect strong auxeticity and how the equivalent micropolar model provides dispersion curves in excellent agreement with the current ones for a wide range of the wave vector magnitude.
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