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 non-linear constitutive model of soft ferromagnets is developed for general magnetomechanical loading histories. The experimental set-up and measured techniques, which were employed to measure the non-linear deformation of both the magnetostrictive materials and the 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; i.e. a convex yield surface can be identified in a stress-magnetic field space, within which the deformation and magnetization are reversible, and increments of both remanent magnetization and remanent strains are normal to the yield surface. The state of materials is described in terms of the remanent strain and the remanent 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 with the measured results. The macroscopic features of ferromagnets, such as hysteresis loop and magnetostrictive hysteresis, are predicted.
