A hysteresis model for ferroelectric ceramics with mechanism for minor loops

In the current paper, the coupled hysteretic behaviors of ferroelectric ceramics subjected to combined electromechanical stimulations are modeled. For a single grain, the polarization orientation switching process is modeled by employing the Euler–Lagrange equations and formulated as a coupled differential equation system. For ferroelectric ceramics, the principle axis orientations of the individual grains are assumed to be distributed in a certain profile, the behaviors of the ceramics are modeled as a weighted combination of the response of each grain. The influence of intergranular interactions is carefully discussed. Numerical results for the minor hysteresis loops in strain and polarization are demonstrated. Comparisons between these results and their experimental counterparts are presented to illustrate the attributes of the proposed model.