**Models**

The further steps in the material modeling should aim to include the hysteresis in both characteristics in a thermodynamic compatible way. Indeed, up to now, this step is made only on one of the two characteristics when the other one is not relevant for the specific applications. This is valid when the vibration source can be considered almost *ideal*.

Another topic in the analysis of a harvester, based on magnetoelastic materials, is the eddy currents effect due to the mechanical stress variations, that can have a detrimental effect on the harvester performances [51]. This phenomenon is present when the material has a finite electric resistivity, that is the case of magnetostrictive materials as Terfenol and Galfenol. The effect can be more harmful on the latter because of the high relative permeability. From the modeling point of view, the eddy currents problem can be formulated, as for standard magnetic materials, starting from Maxwell's equations in the magneto-quasistatic limit. The main difference is that the magnetic characteristics depends on the applied stress. Then, the stress acts as the *forcing term* in the magneto-mechanical problem [14, 15].
