Rate-independent model of ferroelectric materials: finite element and finite difference solution

Ferroelectric materials undergo a phenomenon called domain switching when subjected to electric fields exceeding a critical yielding value: an irreversible polarisation arises, that can be removed only by applying an appropriate electric field in the opposite sense. Under a cyclic electric field, th...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2025-02, Vol.76 (1), Article 36
Main Authors: Alhasadi, Mawafag F., Shahsavari, Leila, Sun, Qiao, Federico, Salvatore
Format: Article
Language:English
Subjects:
Boundary value problems
Elastoplasticity
Electric fields
Ferroelectric materials
Ferroelectricity
Hysteresis loops
Mathematical analysis
Numerical methods
Piezoelectricity
Polarization
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Summary:Ferroelectric materials undergo a phenomenon called domain switching when subjected to electric fields exceeding a critical yielding value: an irreversible polarisation arises, that can be removed only by applying an appropriate electric field in the opposite sense. Under a cyclic electric field, this results in a hysteretic behaviour in the relation between the electric field and the polarisation. The hysteresis loop is a measure of the energy dissipated in the ferroelectric switching process. In this study, we introduce a rate-independent model of ferroelectricity, inspired by small-deformation elastoplasticity models. Analogously to the yielding surface in elastoplasticity, we define the switching surface, the boundary of the domain of the admissible states of the system. States in the interior of the domain are reversible, while states on the surface can be either reversible or irreversible, based on the relation between the electric field and the derivative of the yielding function with respect to the electric field. We solve a two-dimensional benchmark boundary-value problem by applying two numerical methods, Finite Differences and Finite Elements. Our results demonstrate the effectiveness of both methods in capturing the nonlinearities and reproducing the electrical hysteresis loops typical of ferroelectric materials. This work establishes a foundational framework for modelling rate-independent ferroelectricity and paves the way for future research on comprehensive elastoplastic-ferroelectric models for piezoelectric materials.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-024-02348-y