A lumped mass beam model for the wave propagation in anti-tetrachiral periodic lattices

The engineered class of periodic anti-tetrachiral materials is mainly characterized by the unusual macroscopic property of a negative Poisson’s ratio. The auxetic behavior of the material depends on the geometric and elastic features of the microstructure. In particular, the material symmetries of the periodic cell govern the quadratic or orthotropic symmetry of the first-order elastic tensor (i.e. auxetic quadratic or auxetic orthotropy). Under the assumption of uniform mass density and elastic properties, one or the other case can be realized by a square or rectangular microstructure, respectively. A beam lattice model with lumped masses is employed to analyse the effects of different, usually small-valued, geometric and elastic parameters of the high- and low-frequency dispersion curves and band gaps characterizing the free wave propagation.