Modeling of ferroelectric hysteresis as variational inequality

✍ Scribed by Michael Kutter; Anna-Margarete Sändig

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 98 KB
• Volume: 34
• Category: Article
• ISSN: 0936-7195
• DOI: 10.1002/gamm.201110013

✦ Synopsis

Abstract

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)