Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. The formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations are derived using the Dirichlet principle and solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this fascinating effect.
@article{arxiv.1909.08695,
title = {Modelling the flexoelectric effect in solids: a micromorphic approach},
author = {Andrew McBride and Denis Davydov and Paul Steinmann},
journal= {arXiv preprint arXiv:1909.08695},
year = {2023}
}