  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.
