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Two novel chiral block lattice topologies are here conceived havinginteresting auxetic and acoustic behavior. The architectured chiral material ismade up of a periodic repetition of square or hexagonal rigid and heavy blocksconnected by linear elastic interfaces, whose chirality results from an equalrotation of the blocks with respect to the line connecting their centroids. Thegoverning equation of the Lagrangian model is derived and a hermitianeigenproblem is formulated to obtain the frequency band structure. Anequivalent micropolar continuum is analytically derived through a standardcontinualization approach in agreement with the procedure proposed byBacigalupo and Gambarotta (2017) from which an approximation of the frequencyspectrum is derived. Moreover, the overall elastic moduli of the equivalentCauchy continuum are obtained in closed form via a proper condensationprocedure. The parametric analysis involving the overall elastic moduli of theCauchy equivalent continuum model and the frequency band structure is carriedout to catch the influence of the chirality angle and of the ratio between thetangential and normal stiffness of the interface. Finally, it is shown howchirality and interface stiffness may affect strong auxeticity and how theequivalent micropolar model provides dispersion curves in excellent agreementwith the current ones for a wide range of the wave vector magnitude.

Chiral two-dimensional periodic blocky materials with elastic interfaces: auxetic and acoustic properties