Abstract

Ferroelectric ceramics exhibit a spontaneous electric polarization that can be reversed under the application of an electrical or mechanical loading. The macroscopic features of polarization switching derive, at the mesoscale, from the nucleation and growth of domains of constant polarization (these domains correspond to the different variants of the crystallographic phase). Simulations of the evolution of polarization domains are based on diffuse-interface models (also called phase-field models) where the electro-mechanical fields evolve steeply but continuously across domain walls. Existing diffuse-interface models are based on the Allen-Cahn equation which assumes, unlike experimental evidence, a linear relation between the velocity of domain walls and their conjugate driving force. Therefore, while the Allen-Cahn model provides appropriate modelling of polarization switching in the quasistatic regime, it fails to capture rate effects involved in fast-switching experiments. In this work, we develop an alternative phase-field formulation that accounts for the non-linear kinetics of domain walls and discuss its possibilities for modeling the step load response of ferroelectrics as well as the effects of electrical loading rate.