A General Magnetoelastic Coupling Theory of Deformable Magnetized Medium Including Magnetic Forces and Magnetostriction Effects

Abstract

From the viewpoint of energy, a general magnetoelastic coupling theory including magnetic forces and magnetostriction effects is proposed for deformable magnetized medium. Firstly, a Taylor series expansion of independent variables of stress and magnetization in the elastic Gibbs free energy function is applied to obtain a polynomial expression; and then based on the magnetoelastic coupling mechanism, appropriate transcendental functions are substituted for some terms in a polynomial constitutive relationship derived by way of substituting the polynomial Gibbs free energy function in thermodynamic equations to achieve a more compact magnetostrictive constitutive relationship. The numerical simulation exhibits that the predicted magnetostrictive strain and magnetization curves under various pre-stresses are in good agreement with the experimental data given by Kuruzar et al (1971) and Jiles et al (1984). Secondly, based on the above magnetization constitutive relationship, a general magnetic forces expression is presented according to the variational principle for the total energy functional of the coupling system of the 3-d deformable magnetized materials. It is found that for the case of linear isotropic ferromagnetic materials, the magnetic forces expression can be degenerated into the Zhou-Zheng Model (1999). Combining the above nonlinear magnetostrictive constitutive relationship and magnetic forces expression, a general nonlinear magnetoelastic coupling theory is presented in this paper for deformable magnetized medium.