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A model for the description of the energy harvesting in magnetostriction devices is discussed. In particular, the effects of hysteresis, normally observed in these materials, are highlighted and compared to the predictions of the linear modeling. The coupling of the model to the circuit equations leads to a differential equation with hysteresis, which could provide an effective macroscopic description of the energy conversion mechanism taking place in these devices. Numerical tests are performed in order to show the effect of a magnetic field bias on the generated electric power.