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: | Steinmann, Professor Paul and McBride, Professor Andrew |
| 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 |
| Related URLs: |
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