  This paper is concerned with modeling the polarization process in
ferroelectric media. We develop a thermodynamically consistent model, based on
phenomenological descriptions of free energy as well as switching and
saturation conditions in form of inequalities. Thermodynamically consistent
models naturally lead to variational formulations. We propose to use the
concept of variational inequalities. We aim at combining the different
phenomenological conditions into one variational inequality. In our formulation
we use one Lagrange multiplier for each condition (the onset of domain
switching and saturation), each satisfying Karush-Kuhn-Tucker conditions. An
update for reversible and remanent quantities is then computed within one, in
general nonlinear, iteration.
