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Macroscopic description of the non-linear electro-mechanical coupling in ferroelectrics

Bohle U., Kamlah M., Munz D., Tsakmakis C.

Applied Mechanics and Engineering

2000

Vol. 5, no 4

959-970

Our objective is the construction of a phenomenological ferroelectricity model for general electro-mechanical loading histories, which is simple enough to be implemented in an FE-code with reasonable expenditure. In this paper, we motivate and verify the one-dimensional formulation of such a model. This is done by introducing remanent polarization and remanent strain as internal variables besides stress, strain, electric field and polarization. Polarization induced anisotropy is taken into account to the extent deemed necessary. For the sake of simplicity, no rate effects are included. By bilinear approximation the following characteristic phenomena of macroscopic ferroelectricity are represented: dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization, field dependent coercitive stress.