A phenomenological constitutive model for ferromagnetic materials based on rate-independent flow theory

A robust constitutive model is desirable in order to guide the processing and development of ferromagnetism and for use in the design of ferromagnetic devices. In this paper, a phenomenological model of ferromagnets is developed for general magneto-mechanical loading histories. The experimental set-up and measured techniques by which the non-linear deformation of both magnetostrictive and soft ferromagnetic materials subjected to coupled magnetomechanical loading are introduced. The general structure for the constitutive behaviour of ferromagnets including soft-ferromagnetic and hard-ferromagnetic materials is similar to the classical models of metal plasticity. That is, a convex yield surface can be identified in a stress/magnetic field space, within which the deformation and magnetization are reversible; increments of remnant magnetization and remnant strain are normal to the yield surface. The state of materials is described in terms of the remnant strain and the remnant magnetization that are introduced as internal variables besides stress, strain, magnetic field and magnetization. The one-dimensional model is examined by numerical stimulations and the response of the ferromagnetic materials is discussed in comparison to the measured results. The following macroscopic features of ferromagnets, such as hysteresis loop, magnetostrictive, magnetostrictive hysteresis, are predicted.