Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics

Abstract

Our objective is the construction of a phenomenological model of ferroelectricity for general electro-mechanical loading histories, which is simple enough to be implemented in an FE-code with realistic effort. In this paper we motivate and verify the one-dimensional formulation of such a model. It relies upon introducing the remanent polarization and the remanent strain as internal variables besides stress, strain, electric field and polarization. The internal variables are governed by ordinary differential equations. Each of these evolution equations is subjected to two loading conditions of different nature. The first one indicates the onset of changes of the remanent quantities by domain switching, while the second one characterizes the saturation value of a remanent quantity corresponding to a totally switched domain structure. Polarization induced anisotropy is taken into account as far as it seemed necessary. For simplicity, no rate effects are included. The model response to uniaxial electro-mechanical loading histories will be discussed in comparison to known experimental results. By means of a bilinear approximation the following characteristic phenomena of macroscopic ferroelectricity are represented : dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization.