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Coordinate‐invariant phase field modeling of ferro‐electrics, part I: Model formulation and single‐crystal simulations
Author(s) -
Schrade D.,
Keip M.A.,
Thai H.,
Schröder J.,
Svendsen B.,
Müller R.,
Gross D.
Publication year - 2015
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201510005
Subject(s) - isotropy , phase field models , evolution equation , ferroelectricity , transverse isotropy , materials science , microstructure , invariant (physics) , field (mathematics) , finite element method , phase (matter) , physics , condensed matter physics , mechanics , thermodynamics , mathematical analysis , mathematics , mathematical physics , composite material , pure mathematics , optics , quantum mechanics , optoelectronics , dielectric
An electro‐mechanically coupled phase field model for ferroelectric domain evolution is introduced. Based on Gurtin's concept of a microforce balance, a generalized Ginzburg‐Landau evolution equation is derived from the second law of thermodynamics. The thermodynamic potential is formulated for transversely isotropic material behavior by adopting a coordinateinvariant formulation. The model is reduced to 2D and implemented into a finite element framework. The numerical simulations concern the microstructure evolution in mechanically clamped BaTiO 3 single‐crystals. In the second part of this contribution Keip et al. [1], the poling behavior of ferroelectric composites and polycrystals is investigated with regard to size effects and the influence of a discontinuous order parameter field across grain boundaries. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)