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摘要
This paper presents a general theoretical model of constitutive relationships for the soft ferromagnetic and/or the giant magnetostrictive rods under a prestress and a bias magnetic field on the basis of Gibbs' free energy function. After Gibbs' free energy function is expanded by Taylor's series expansion with the stress and the magnetization in the materials as the independent variables, a transcendental function is appropriately selected to replace the first terms with higher order up to six on the basis of the meaning of mechanics and physical theory of magnetic domains, from which a set of closed and analytical expressions of the constitutive relationships for the soft ferromagnetic material rods are obtained, and the parameters appearing in the relationships are determined by those measurable experiments in mechanics and physics. It is found that the predictions from this model are in good accordance with the experimental data given by Kuruzar and Cullity [Int. J. Magn. 1, 323 (1971)] and Jiles and Atherton [J. Phys. D 17, 1265 (1995)] and that this model can be degenerated into the relevant constitutive relationships for the giant magnetostrictive materials obtained by Zheng and Liu [J. Appl. Phys. 97, 053901 (2005)]. Comparing this model with other existing models in this field, the quantitative results exhibit that the relationships obtained here are more effective to describe the effect of the prestress on the magnetostrictive strain and the magnetization, and the effect of the stress and the magnetic field on Young's modulus.
