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Modeling of ferroelectric hysteresis as variational inequality
Author(s) -
Kutter Michael,
Sändig AnnaMargarete
Publication year - 2011
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.201110013
Subject(s) - variational inequality , ferroelectricity , hysteresis , polarization (electrochemistry) , electric field , inequality , field (mathematics) , point (geometry) , mathematics , materials science , physics , mathematical analysis , statistical physics , condensed matter physics , geometry , pure mathematics , chemistry , quantum mechanics , dielectric
Ferroelectric materials are characterized by interaction‐effects of mechanical and electrical fields due to different polarization directions of the unit cells. The relations between polarisation and electric field and mechanical strain and electric field respectively can be described by hysteresis curves. Some models, which describe the ferroelectric material behaviour, e.g. [3], [8], rely on concepts close to elastoplasticity. We use these ideas and derive variational evolution inequalities analogously to elastoplastic models discussed in [1]. Based on these inequalities we formulate equivalent mathematical problems and get some existence results. The formulation of variational evolution inequalities is a good starting point for numerical methods similar to elastoplasticity (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)