Modelling the flexoelectric effect in solids: a micromorphic approach

TL;DR

This paper introduces a micromorphic finite element model to accurately simulate the complex, nonlinear flexoelectric effect in dielectric solids, capturing the coupling between mechanical, electrical, and gradient fields.

Contribution

It presents a novel micromorphic formulation that incorporates higher-order gradient effects in a finite element framework for flexoelectricity, including all relevant nonlinearities.

Findings

The model successfully captures the nonlinear flexoelectric response.

Numerical examples demonstrate the method's ability to simulate complex behaviors.

The approach provides new insights into the flexoelectric effect in solids.

Abstract

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.