  The use of multifunctional composite materials adopting piezo-electric
periodic cellular lattice structures with auxetic elastic behavior is a recent
and promising solution in the design of piezoelectric sensors. In the present
work, periodic anti-tetrachiral auxetic lattice structures, characterized by
different geometries, are taken into account and the mechanical and
piezoelectrical response are investigated. The equivalent piezoelectric
properties are obtained adopting a first order computational homogenization
approach, generalized to the case of electro-mechanical coupling, and various
polarization directions are adopted. Two examples of in-plane and out-of-plane
strain sensors are proposed as design concepts. Moreover, a
piezo-elasto-dynamic dispersion analysis adopting the Floquet-Bloch
decomposition is performed. The acoustic behavior of the periodic piezoelectric
material with auxetic topology is studied and possible band gaps are detected.
