Modelling the flexoelectric effect in solids: A micromorphic approach
McBride AT, Davydov D, Steinmann P (2020)
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 371
Article Number: 113320
DOI: 10.1016/j.cma.2020.113320
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 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.
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APA:
McBride, A.T., Davydov, D., & Steinmann, P. (2020). Modelling the flexoelectric effect in solids: A micromorphic approach. Computer Methods in Applied Mechanics and Engineering, 371. https://doi.org/10.1016/j.cma.2020.113320
MLA:
McBride, A. T., Denis Davydov, and Paul Steinmann. "Modelling the flexoelectric effect in solids: A micromorphic approach." Computer Methods in Applied Mechanics and Engineering 371 (2020).
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