The most known empirical models in hysteresis are Preisach and Jiles-Atherton models. These models allow an accurate modeling of the hysteresis loop and are widely used in the industry. However, these models lose the connection with thermodynamics and the energy consistency is not ensured. A more recent model, with a more consistent thermodynamical foundation, is  the vectorial incremental nonconservative consistent hysteresis (VINCH) model of Lavet et al. (2011)