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Modeling of ferroelectric hysteresis as variational inequality. (English) Zbl 1239.74027

Summary: 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, rely on concepts close to elastoplasticity. We use these ideas and derive variational evolution inequalities analogously to elastoplastic models discussed by W. Han and B. D. Reddy [Plasticity. Mathematical theory and numerical analysis. Interdisciplinary Applied Mathematics. 9. New York, NY: Springer (1999; Zbl 0926.74001)]. 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.

MSC:

74F15 Electromagnetic effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
49J40 Variational inequalities

Citations:

Zbl 0926.74001
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References:

[1] W. Han B. Reddy Plasticity, Mathematical Theory and Numerical Analysis , Springer-Verlag 1999.
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