Modelling the flexoelectric effect in solids: A micromorphic approach - McBride, A. T.; Davydov, Denis; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2020)
Flexoelectricity is characterised by the coupling of the second gradient of the motion and the electrical field in a dielectric material. The presence of the second gradient is a significant obstacle to obtaining the approximate solution using conventional numerical methods, such as the finite element method, that typically require a C1-continuous approximation of the motion. 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. Our 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 is derived using the Dirichlet principle and approximately solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this intriguing effect that underpins or influences many important scientific and technical applications.
CRIS-Team Scopus Importer:2020-08-28
Keywords: Finite element method; Flexoelectricity; Micromorphic continua