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

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 e}ort[ 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\ strainelectric _eld and polarization[ The internal variables are governed by ordinary di}erential equations[ Each of these evolution equations is subjected to two loading conditions of di}erent nature[ The _rst 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 e}ects 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 piezoelectricitybutter~y hysteresis\ ferroelastic hysteresis\ mechanical depolarization[ 0887 Elsevier Science Ltd[ All rights reserved[