  When subjected to electro-mechanical loading, ferroelectrics see their
polarization evolve through the nucleation and evolution of domains. Existing
mesoscale phase-field models for ferroelectrics are typically based on a
gradient-descent law for the evolution of the order parameter. While this
implicitly assumes that domain walls evolve with linear kinetics, experiments
instead indicate that domain wall kinetics is nonlinear. This, in turn, is an
important feature for the modeling of rate-dependent effects in polarization
switching. We propose a new multiple-phase-field model for ferroelectrics,
which permits domain wall motion with nonlinear kinetics, with applications in
other solid-solid phase transformation problems. By means of analytical
traveling wave solutions, we characterize the interfacial properties (energy
and width) and the interface kinetics of straight domain walls, as furnished by
the general kinetics model, and compare them to those of the classical
Allen--Cahn model. We show that the proposed model propagates domain walls with
arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ
for the different types of domain walls in accordance with experimental
evidence.
