Magnetomechanical Coupling Constitutive Relation Of Magnetostrictive Materials

Simulation of magneto-mechanical coupling constitutive relation and the predictive results from constitutive model of giant magnetostrictive materials play important role in research and development of magnetic field actuated sensors and actuators. This paper constructs a magneto-mechanical coupling constitutive model for magnetostrictive materials.Firstly, based on a well discussed formal constitutive model, the strain of the magnetostrictive material is divided into three parts, the linear strain, ferroelastic strain and the magnetostriction strain. Refers to the ferroelasticity of the material, the strain-stress relation is obtain by combining the classical statistical theory and the domain rotation under the action of stress anisotropy field. This relationship is always depicted by a hypothetical function in most of the constitutive models proposed before. A one dimensional magneto-mechanical coupling constitutive model of magnetostrictive materials is proposed by using the generalized Hook’s theorem, ferroelastic strain and the magnetostrictive strain expression proposed in D-H model. Secondly, the constitutive model proposed above is applied to the polycrystalline system. Taking into account the anisotropic initial state of the orientational solidified polycrytals, an equivalent initial stress is adopted to describe the anisotropy. With this assumption, the constitutive model is generalized into the polycrystalline, and rational explanations are made on the relevant experimental results. Finally, the generalized model is applied to calculate the magnetostriction, magnetization, strain-stress relation and the ΔE effects of giant magnetostrictive materials. The result from the theory is in agreement with the recent experiments which suggest the validity of the theory. In addition, the constitutive model is based on the theoretical framework of domain rotation, and hence, it is helpful for understanding the microscopic mechanism of magneto-mechanical coupling.The model is based on the D-H model and the Z-L model, but we have made some progress on theoretical description of ferroelasticity and have extended the model into the polycrystalline case. Furthermore, the magnetization and the ferroelastic strain are modeled in a same theoretical framework.