Thermodynamical analysis of hysteresis in rigid ferroelectric bodies ZAMP-D-21-00505R1

We propose a nonlinear thermoelectric framework adequate for capturing the phenomenon of electrical hysteresis in ferroelectric materials. We call this formulation rate-independent ferroelectricity , because the rate of polarisation is linear in the rate of the electric field, so that the process is independent of the time scale. This is inspired by the theory of rate-independent plasticity in the early form proposed by Green and Naghdi (Arch Ration Mech Anal 18:251–281, 1965) and Kratochvil and Dillon (J Appl Phys 40(8):3207–3218, 1969), whose works were in turn based on the formulation of thermodynamics with internal variables by Coleman and Gurtin (J Chem Phys 47:597–613, 1967). We impose thermodynamical restrictions on the proposed constitutive equations in order to guarantee positive dissipation under irreversible switching (domain switching). Finally, we illustrate the proposed framework with the numerical solution of a one-dimensional example, in which a cyclic electric field is applied, resulting in a ferroelectric polarisation-electric field hysteresis loop. The novelty of this work is in the use of an analogue of the evolution law proposed by Green and Naghdi (1965) to simulate the electrical hysteresis behaviour in ferroelectric materials, caused by domain wall motion under cyclic electric loadings. This hysteresis loop eventually results in a significant residual electric polarisation.