Control of the piezoelectric and flexoelectric homogenized properties of architected materials by tuning their inner topology

The present contribution aims to study the effect the inner topology of periodic architected materials on their effective piezoelectric and flexoelectric properties. An analysis is performed to study the sensitivity of the effective flexoelectric moduli to the geometrical variables of the considered unit cells of periodic lattice materials. More specifically, hexagonal, re-entrant auxetic, and rectangular unit cells are investigated in terms of their relative piezoelectric and flexoelectric response. The base material obeys a piezoelectric behavior, and the homogenized electromechanical properties are evaluated using the extended Hill-Mandel macrohomogeneity condition articulated with variational principles in the context of periodic multiphysical homogenization. The developed modeling framework of coupled electromechanical phenomena accounts for the higher gradient effects modeled by flexoelectricity that are induced by the strong gradient of properties that exist at the microlevel of the lattice unit cell. Regular hexagonal, re-entrant hexagonal and rectangular lattice unit cells are mutually compared in terms of their flexoelectric properties. The regular hexagonal UC shows the highest piezoelectric moduli, whereas the flexoelectric moduli are found to be maximum for the re-entrant UC. The coupling between mechanical and electrical fields is attested by the non-uniform distribution of the electric potential within the three studied architected materials subjected to a uniform strain.