A non-isothermal phase-field model for piezo-ferroelectric materials

We propose a model for the study of piezo-ferroelectric materials, based on the Ginzburg-Landau approach to the ferroelectric transition, in which the inelastic deformation is a direct function of the ferroelectric polarization. The non-isothermal effects related to the phase change and other dissipative phenomena are considered by a suitable energy balance equation, according to the restrictions of the second principle. The hysteresis phenomena for polarization and inelastic strain are considered from both the energetic perspective of the vector Ginzburg-Landau equation and the dissipation-dominated perspective of the rate-independent evolutionary equations.