Phenomenological modeling of the non-linear electromechanical coupling in ferroelectrics

Our objective is the construction of a phenomenological model of ferroelect ricity for general electromechanical loading histories, which is simple eno ugh 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 re lies upon introducing the remanent polarization and the remanent strain as internal variables besides stress, strain, electric held and polarization. The internal variables are governed by ordinary differential equations. Eac h of these evolution equations is subjected to two loading conditions of di fferent nature. The first one indicates the onset of changes of the remanen t quantities by domain switching, while the second one characterizes the sa turation value of a remanent quantity corresponding to a totally switched d omain structure. Polarization induced anisotropy is taken into account as f ar 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 bilin ear approximation the following characteristic phenomena of macroscopic fer roelectricity are represented: dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization. (C) 1998 Elsevier Science Ltd. All rights reserved.