Modelling the flexoelectric effect in solids: a micromorphic approach

Andrew McBride; Denis Davydov; Paul Steinmann

doi:10.1016/j.cma.2020.113320

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arXiv · 1909.08695

Modelling the flexoelectric effect in solids: a micromorphic approach

Andrew McBride·Denis Davydov·Paul Steinmann

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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.

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Andrew McBride, Denis Davydov, Paul Steinmann. 2019-08-20. Modelling the flexoelectric effect in solids: a micromorphic approach. https://doi.org/10.1016/j.cma.2020.113320

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