Scale transition and residual fields in modeling of polycrystalline ferroelectrics based on the internal energy potential and a Voigt–Reuss approximation

Abstract

A multiscale constitutive model, implemented within a semi-analytical computational framework, is presented. Accounting for domain switching in a tetragonal lattice and electromechanical intergranular interactions, it aims to accurately reproduce experimental data available from butterfly and dielectric hysteresis loops. For the sake of validation, these have been collected from various sources providing ranges of values for characteristic quantities. Adopting the fundamental ideas of a previously published model, a different homogenization approach is employed for the transition from grain to polycrystalline domain, providing both residual stress and electric fields. Furthermore, the thermodynamic driving force and constitutive equations on the grain level are based on a different thermodynamical potential. While the modeling approach inherently does not include any tuning parameters, the introduction of one and two, respectively, additional parameters is investigated, although computational results are basically in good agreement with experimental ranges.