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For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.

For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magnetomechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

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