基于唯象相变理论的磁致伸缩材料耦合滞回动力学模拟

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.

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

In the current paper, a coupled nonlinear differential equation is proposed to model the hysteretic dynamics of one-dimensional magnetostrictive 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 switchings and magneto-strain. Each of its minima is associated with one of the magnetization orientations in materials. Nonlinear constitutive laws accounting for magnetostriction effects are obtained by using thermodynamic equilibrium conditions. The hysteretic loops and butterfly-shaped behaviors in the magnetic and mechanical fields are both successfully modeled. Comparison of the model results with its experimental results reported in literatures is presented, capability of the model is approved.