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 obtained. 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.

这里设想了两种新颖的手性嵌段晶格拓扑结构，其具有有趣的通行和声学行为。结构化的手性材料由通过线性弹性界面连接的方形或六边形刚性块和重块的周期性重复构成，其手性来自于块相对于连接其质心的线的相等旋转。推导了拉格朗日模型的控制方程，并提出了厄米特征问题来获得频带结构。通过与Bacigalupo和Gambarotta（2017）提出的程序一致的标准连续化方法，可以分析得出等效的微极连续体，从中可以获得频谱的近似值。此外，等效柯西连续体的整体弹性模量通过适当的缩合程序以封闭形式获得。进行了涉及柯西等效连续体模型的整体弹性模量和频带结构的参数分析，以捕获手性角以及界面的切向刚度和法向刚度之比的影响。最后，显示了手性和界面刚度如何影响强膨胀性，以及等效的微极性模型如何在广泛的波矢量幅值范围内提供与当前曲线极好的一致性的色散曲线。进行了涉及柯西等效连续体模型的整体弹性模量和频带结构的参数分析，以捕获手性角以及界面的切向刚度和法向刚度之比的影响。最后，表明手性和界面刚度如何影响强膨胀性，以及等效的微极性模型如何在宽范围的波矢量幅值范围内提供与当前曲线极好的一致性的色散曲线。进行了涉及柯西等效连续体模型的整体弹性模量和频带结构的参数分析，以捕获手性角以及界面的切向刚度和法向刚度之比的影响。最后，表明手性和界面刚度如何影响强膨胀性，以及等效的微极性模型如何在宽范围的波矢量幅值范围内提供与当前曲线极好的一致性的色散曲线。