Multiscale Modeling of Magnetic Materials

International audienceFerromagnetic materials are used in a wide range of applications such as sensors, actuators, motors or transformers. Their main property of interest is their capability to reach high magnetisation levels when subjected to an external magnetic field of relatively low intensity. This property originates in the complex magnetic domain microstructure and its evolution under the application of external loading. In that sense, magnetic behaviour is a very good example of multiscale phenomena, and a natural playground for multiscale modelling approaches. Of course the magnetisation curve can be described using macroscopic approaches [1], and such macroscopic approaches are necessary when it comes to numerical design of engineering parts or devices. However, because magnetic behaviour is very sensitive to many external influences-such as temperature, chemical environment , or mechanical stress-macroscopic approaches can quickly become inoperative to describe these coupled phenomena intricately related to the mi-crostructure and its evolution. On the other hand, if the objective is to understand with more precision the formation and evolution of domain microstructures, mi-cromagnetic approaches [2], which consider the energetic equilibrium at the scale of a set of atoms, can provide a very powerful insight into the mechanisms of ferromagnetism. Their implementation for the design of electromagnetic devices remains however most of the time out of reach. This chapter is dedicated to multiscale approaches for the modelling of magnetic behaviour. These approaches stand between micromagnetic and macro-scopic approaches. The objective is to link the basic mechanisms responsible for magnetic behaviour to the macroscopic response of ferromagnetic materials to external loadings. An emphasis will be given on the possible ways to make use of these multiscale approaches for the numerical modelling of practical engineering devices. The approach will be illustrated on applications involving magneto-mechanical coupling effects