Phase Field Simulations of Hysteresis and Butterfly Loops in Ferroelectrics Subjected to Electro‐Mechanical Coupled Loading

Abstract

Two‐dimensional computer simulations of ferroelectric polarization switching have been performed using the phase field simulation model developed by employing the time‐dependent Ginsburg–Landau equations. The bulk‐free energy, polarization gradient energy, long‐range dipole–dipole electrostatic interactions, and elastic energy were taken into account in the above‐mentioned simulations. The influences of electric–mechanical coupled loading on the hysteresis and butterfly loops were studied. The results showed that the coupled electro‐mechanical loading could change both the coercive field of ferroelectric materials and the symmetry of hysteresis and butterfly loops.