Continuum and computational modeling of flexoelectricity in nanomaterials: A review

Abstract

The ability of certain dielectric materials to convert electrical stimuli into mechanical deformation, i.e., piezoelectricity, is a remarkable property limited to a small subset of non-centrosymmetric materials. In contrast, flexoelectricity is a universal phenomenon: all dielectrics can exhibit polarization in response to strain gradients and, conversely, experience mechanical deformation under non-uniform electric fields. While the intrinsic magnitude of the flexoelectric effect is typically small, its influence on the thermodynamic behavior of materials becomes significant, and often dominant, at the nanoscale. This review highlights recent advances in continuum modeling and computational approaches that aim to deepen the understanding of flexoelectricity in both solid and soft materials. We provide a detailed discussion of the fundamental mechanisms, developments in phenomenological and continuum frameworks, and key recent findings. Finally, we outline potential future research directions for the computational modeling of flexoelectricity and its diverse applications. © 2025 Author(s).