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Modelling the flexoelectric effect in solids: a micromorphic approach. (English) Zbl 1506.74121

Summary: 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 \(C^1\)-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.

MSC:

74F15 Electromagnetic effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics

Software:

deal.ii; Trilinos; ADOL-C
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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