Electroelastic equations describing slow hysteresis in polarized ferroelectric ceramic plates

Abstract

Rotationally invariant electroelastic equations are extended to account for slow hysteretic effects in polarized ferroelectric ceramic plates by employing an internal variable in a thermodynamic state function. All material irreversibility is taken to be a consequence of the ferroelectric polarization-electric-field irreversibility. Since we are concerned with the slowest possible hysteresis, we ignore the evolution equation and take the known irreversible thickness polarization-electric-field saturation curve as the starting curve. After the general nonlinear three-dimensional equations are obtained, they are reduced to linear strain and then plane stress because all experimental data available to us are from strain measurements on a thin wide beam forced by voltages applied to very thin polarized ferroelectric ceramic actuators on the surfaces. The new irreversible material coefficients are obtained from data on one major hysteresis loop along with the coefficients in the saturation polarization-electric-field relation. These now known coefficients are then used to calculate other hysteresis loops, which are shown to agree quite well with measurement.