A nonlinear constitutive model for Terfenol-D rods

To overcome some deficiencies in previous constitutive models of giant magnetostrictive materials, a nonlinear and coupled model is suggested to describe the constitutive relations for a Terfenol-D rod subjected to an axial pre-stress and then located in an axial magnetic field. The numerical simulation by the model proposed in this paper shows predicted magnetostrictive strain curves for various compressive pre-stresses in good agreement with the experimental data not only in the region of low and moderate magnetic field but also in the region of high field. In comparison with the previous models, the proposed model can more effectively describe the effect of the pre-stress on the maximum magnetostrictive strain. Moreover, the effect of the stress and the magnetic field on the Young’s modulus of the materials, i.e., the ΔE effect, can also be predicted. In the proposed model, there are only five material parameters. They are the saturation magnetization Ms, the saturation magnetostrictive strain λs, the intrinsic (or saturation) Young’s modulus Es and the initial Young’s modulus E0 as well as the linear magnetic susceptibility χm. Since these parameters are easily measured in experiments, the proposed model is convenient to be used in engineering applications.