磁致伸缩材料的非线性本构关系

NONLINEAR CONSTITUTIVE RELATIONS FOR MAGNETOSTRICTIVE MATERIALS

给出了磁致伸缩材料的两个非线性本构关系，即标准平方型和双曲正切型．在确定一维问题的本构系数时，基于已有的实验结果，引进一个材料函数，用来描述磁致伸缩材料的压磁系数随预应力变化的关系．将非线性本构关系的理论模型计算结果与实验曲线对比，结果表明标准平方型本构关系在中低磁场下能精确地模拟实验曲线，而双曲正切型本构关系在高磁场时能反映材料的磁致应变饱和现象．讨论了标准平方型本构的一般三维情形，给出了确定本构系数的方法．

The magnetostrictive materials usually endure a coupled mechanical-magnetic field when they are in application. Their constitutive relation is essentially nonlinear. From the energy balance equation of electric-magnetic body, by means of the Faraday electric-magnetic induction law and the assumption of magnetostatic approximation, we present two nonlinear constitutive relations of magnetostrictive materials which are called Standard Square and Hyperbolic Tangent models, respectively. Basically, the micro-mechanism of magnetostriction can help understand the nonlinearity of magnetostrictive materials and characterize the moduli in the constitutive relation. When a magnetic field is applied, the magnetic domains will switch to the direction parallel to the external magnetic field. At the same time, the material exhibits elongation in the direction of external magnetic field. Another driving force is the external stress. Upon being applied an external load, the magnetic domains will also switch continuously to the direction perpendicular to the external force. In the meantime, magnetocrystalline anisotropy will retard the rotation of magnetic domains. Thus, the external force must be strong enough to overcome the magnetocrystalline anisotropy effect. There exist different critical stresses for different magnetostrictive materials. To characterize the moduli in the constitutive relations for the one-dimensional problem, we introduce one material function to describe the relation between the external magnetic field associated with the peak piezomagnetic coefficient and the compressive pre-stress based on the published experimental results. The accuracy of the nonlinear constitutive relations is evaluated by comparing the theoretical predictions with experimental results obtained on a Terfenol-D rod operated under both a compressive pre-stress and a bias magnetic field. Results indicate that the Standard Square constitutive relation can accurately predict the experimental results in both the low and the medium magnetic fields, while the Hyperbolic Tangent constitutive relation can reflect the trend of saturation of magnetostrictive strain in the high region of the applied magnetic field. Furthermore, we discuss the Standard Square constitutive relations of the general three-dimension case. For isotropic magnetostrictive materials, a proposed method is presented to characterize the modulus tensors.