A coupled structural-magnetic strain and stress model for magnetostrictive transducers

This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a "law of approach" to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is demonstrated that the model accurately characterizes the magnetic hysteresis in the material, as well as the strains and forces output by the transducer under conditions typical of engineering applications.