Vol.12, No.3, 2009, pp.237-250, doi:10.3970/cmc.2009.012.237
OPEN ACCESS
ARTICLE
A General Magnetoelastic Coupling Theory of Deformable Magnetized Medium Including Magnetic Forces and Magnetostriction Effects
• Hao-Miao Zhou1,2, You-He Zhou1, Xiao-Jing Zheng1, Jing Wei3
Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, P. R. China. Tel: 086-0931-8910340; email: zhouyh@lzu.edu.cn
Department of Electronics and Information Engineering, College of Information Engineering, China Jiliang University, Hangzhou, 310018, P. R. China.
College of Foreign Languages, Zhejiang Gongshang University, Hangzhou, 310018, P. R. China
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.
Keywords
Magnetoelastic coupling, Magnetic forces, Magnetostriction effects