ELECTROELASTIC EQUATIONS DESCRIBING SLOW HYSTERESIS IN POLARIZED FERROELECTRIC CERAMIC PLATES

Rotationally invariant electroelastic equations are extended to accoun t for slow hysteretic effects in polarized ferroelectric ceramic plate s by employing an internal variable in a thermodynamic state function. All material irreversibility is taken to be a consequence of the ferr oelectric polarization-electric-field irreversibility. Since we are co ncerned with the slowest possible hysteresis, we ignore the evolution equation and take the known irreversible thickness polarization-electr ic-field saturation curve as the starting curve. After the general non linear three-dimensional equations are obtained, they are reduced to l inear strain and then plane stress because all experimental data avail able to us are from strain measurements on a thin wide beam forced by voltages applied to very thin polarized ferroelectric ceramic actuator s on the surfaces. The new irreversible material coefficients are obta ined from data on one major hysteresis loop along with the coefficient s in the saturation polarization-electric-field relation. These now kn own coefficients are then used to calculate other hysteresis loops, wh ich are shown to agree quite well with measurement. (C) 1998 American Institute of Physics. [S0021-8979(98)03210-1]