Modelling the flexoelectric effect in solids: a micromorphic approach

McBride, A. , Davydov, D. and Steinmann, P. (2020) Modelling the flexoelectric effect in solids: a micromorphic approach. Computer Methods in Applied Mechanics and Engineering, 371, 113320. (doi: 10.1016/j.cma.2020.113320)

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Abstract

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 -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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Professor Andrew and Steinmann, Professor Paul
Authors: McBride, A., Davydov, D., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:19 August 2020
Copyright Holders:Copyright © 2020 The Author(s)
First Published:First published in Computer Methods in Applied Mechanics and Engineering 371:113320
Publisher Policy:Reproduced under a Creative Commons license
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment