Magnetic losses in a ferromagnetic lamination can be separated into three contributions. Bertotti theoretically assessed this distribution at the end of the 20th century in the Statistical Theory of Losses (STL), triggering significant progress in understanding the dissipation mechanisms. Recent studies have shown the possibility of reconstructing a hysteresis cycle from the high-frequency Barkhausen noise signal. Applying STL to the Barkhausen noise cycles has never been done before. Still, it could help establish a parallel with the measurement of the magnetization cycle versus frequency and the energy loss. However, STL analysis in its ultimate description requires sinusoidal flux density, while Barkhausen noise measurements are usually done with a constant excitation slope. Multiple magnetic flux density control methods were described in the literature and are reviewed in this manuscript. However, the Barkhausen noise context, requiring high-frequency sampling during the magnetization cycle, is more constraining. Therefore, specific performance criteria were considered, followed by numerical tests to determine the most adapted method to a Barkhausen STL description. Eventually, the Proportional Iterative Learning Control (P-ILC) gave the highest satisfaction rate and was chosen for experimental tests. Some of these experimental results are provided in the manuscript discussion together with suggestions for convergence speed improvement. It is, for instance, recommended to increase the gain near saturation, where the system response is poor.

Giant magnetostrictive materials such as Terfenol-D and Galfenol are used to design actuators and sensors, converting magnetic input into a mechanical response, or conversely, mechanical input into a magnetic signal. Under standard operating conditions, these materials are subjected to stress. It is therefore important to be able to measure, understand and describe their magneto-mechanical behaviour under stress. In this paper, a comprehensive characterisation of the anhysteretic magneto-mechanical behaviour of Terfenol-D was performed. An energy-based multiscale approach was applied to model this behaviour. Finally, it was shown that the strain behaviour of Terfenol-D can be satisfactorily described using an analytical model derived from the full multiscale approach.

The influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach, and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.