A thermodynamically consistent model with evolving domain structures in ferroelectrics

A thermodynamically consistent uniaxial model combining the benefits of both phenomenological and micromechanical models is proposed. The driving forces derived from irreversible thermodynamics induce domain switching on reaching certain critical values. The back stress and electric fields, assumed as linear functions of remanent strain and polarization, developed by the domain switching process are introduced to assist or resist further changes in microscopic state of the crystal depending on the loading history. In this model, volume fractions of three distinct uniaxial variants act as internal variables describing the microscopic state of the crystal. Domain switching process for general cases involving two variants and for simultaneous evolution cases where three distinct variants participate the switching process are dealt with. The model is found to reproduce the characteristics of the responses of ferroelectric polycrystals under uniaxial complex electro-mechanical loading cases that are consistent with the experimental observations.