基于唯象相变理论的磁致伸缩材料耦合滞回动力学模拟

Modeling the Dynamic Hysteretic Behavior in Magnetostrictive Materials Based on the Phenomenological Theory of Phase Transition

论文基于改进的Landau唯象相变理论,构造一个耦合的非线性常微分方程模型来模拟一维磁致伸缩材料的磁滞动态特性.模型的构造通过引入一个非凸的自由能函数来模拟磁致伸缩磁材料中不可逆的磁极化翻转与磁致应变,该自由能函数的每一个局部极小值都对应材料的一个磁化方向.通过热力学平衡条件建立能刻画磁致伸缩效应的非线性本构关系.所构造的模型成功地模拟出了磁场与弹性场之间的磁滞曲线和蝶形曲线,并采用实验结果对模型进行了验证.

Due to their inherent magnetomechanical coupling properties,nowadays the magnetostrictive materials are widely used in many applications.However,when the magnetostrictive materials are considered for device design and control applications,it is necessary to take into account that they typically operate in a nonlinear manner and hysteresis exists in the input-output relations.To take full advantages of the materials＇ properties,as well as to analyze,control,and optimize the magnetostrictive devices,an efficient model which can capture the complex nonlinearities with coupled hysteretic effects is essential.In the current paper,a coupled nonlinear differential equation is proposed to model the hysteretic dynamics of one-dimensionalmagnetostrictive materials based on the modified Landau phenomenological theory of phase transition.A non-convex free energy function is constructed to model the irreversible magnetization orientation switching and magneto-strain.Each of its minima is associated with one magnetization orientation in the materials.The nonlinear constitutive laws accounting for magnetostriction effects are obtained by using the conditions of thermodynamic equilibrium.The hysteretic loops and butterfly-shaped behaviors in the magnetic and mechanical fields are both successfully modeled.Comparison of the model results with the experimental results reported in literature is presented,and the capability of the model is verified.By applying the proposed differential equation model for hysteretic dynamics,the numerical expenses have been largely reduced as compared to other models,whilst the accuracy is very satisfactory.These facts indicate that the current model leads to more efficient implementations,which are of particular importance for the model-based control theory and applications when the magnetorestrictive materials are involved.