Phase field simulations of low-dimensional ferroelectrics

A coupled theory of nonlinear electro-thermo-viscoelasticity with inclusion of hysteresis, aging and damage effects is developed based on non-equilibrium thermodynamics. In consideration of the Gibbs free energy including the contribution of the free electric field as a functional of the histories of stress, temperature, temperature gradient and electric field in the reference configuration with damage being introduced as an internal state variable, constitutive relations and kinetic laws are obtained from the energy balance equation and the entropy production inequality. Finite electro-thermo-viscoelasticity and nonlinear electro-thermo- elasticity can be taken as special cases. A superposition principle of time, aging, temperature, stress and electric field is proposed for materials with memory on an intrinsic time scale so that the long-term property functions may be represented with horizontal and vertical shifting of the momentary master curves. This formulation lays a foundation for the characterization of the short- and long-term behavior of time-dependent materials with evolving damage under combined electric, thermal and mechanical loadings.