Competition of piezo- and flexoelectricity in metamaterials

Flexoelectricity and piezoelectricity provide two distinct pathways for electromechanical coupling: the former originates from strain gradients and is present in all dielectrics, whereas the latter is a linear coupling effect restricted to non-centrosymmetric materials. This paper numerically investigates the combined flexoelectric and piezoelectric behavior of architected microstructures (metamaterials). In metamaterials, geometric features can be tailored to generate pronounced bending and strain gradients even under macroscopically uniform loading. This work investigates metamaterials whose topologies are intentionally designed to amplify strain gradients and thereby activate flexoelectricity at micro- and nanoscales. To study the interplay between flexoelectric and piezoelectric effects, we assign dielectric or piezoelectric material properties to the same architected geometries and employ a mixed finite element formulation that incorporates mechanical strain, strain gradients, electric fields, and their linear and higher-order couplings. In this way, the combined response is realized through the superposition of topology-induced flexoelectricity and intrinsic piezoelectric material coefficients. Verification against existing metamaterial designs demonstrates that our framework accurately reproduces apparent piezoelectricity in centrosymmetric dielectrics. Parametric studies reveal that flexoelectricity dominates at small geometric length scales, while piezoelectricity prevails at larger scales; depending on the architecture, their interaction can either enhance or suppress the net electrical output. These findings provide insight into how geometry and material length scales govern the electromechanical behavior of architected dielectrics and offer guidelines for designing next-generation micro- and nanoscale energy harvesters and sensing devices.