A Nonlinear Magneto-Mechanical Coupled Constitutive Model for the Magnetostrictive Material Galfenol

In order to predict the performance of magnetostrictive smart material and push its applications in engineering, it is necessary to build the constitutive relations for the magnetostrictive material Galfenol. For Galfenol rods under the action of the pre-stress and magnetic field along the axial direction, the one-dimensional nonlinear magneto-mechanical coupling constitutive model is proposed based on the elastic Gibbs free energy, where the Taylor expansion of the elastic Gibbs free energy is made to obtain the polynomial forms. And then the constitutive relations are derived by replacing the polynomial forms with the proper transcendental functions based on the microscopic magneto-mechanical coupling mechanism. From the perspective of microscopic mechanism, the nonlinear strain related to magnetic domain rotation results in magnetostrictive strain changing with the pre-stress among the elastic strains induced by the pre-stress. By comparison, the predicted stress-strain, magnetostrictive strain, magnetic induction and magnetization curves agreed well with experimental results under the different pre-stresses. The proposed model can describe not only the influences of pre-stress on magnetostrictive strain and magnetization curves, but also nonlinear magneto-mechanical coupling effect of magnetostrictive material systematically, such as the Young's modulus varying with stress and magnetic field. In the proposed constitutive model, the key material constants are not chosen to obtain a good fit with the experimental data, but are measured directly by experiments, such as the saturation magnetization, saturation magnetostrictive coefficient, saturation Young's modulus, linear magnetic susceptibility and so on. In addition, the forms of the new constitutive relations are simpler than the existing constitutive models. Therefore, this model could be applied conveniently in the engineering applications.