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本文基于改进的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。
Based on the improved Landau phenomenal phase transition theory, a coupled nonlinear ordinary differential equation model is constructed to simulate the hysteresis dynamics of one-dimensional magnetostrictive materials. The model is constructed by introducing a nonconvex free energy function to simulate irreversible magnetic reversal and magnetostriction in magnetostrictive magnet materials. Each local minimum of the free energy function corresponds to a magnetization direction of the material. Through the thermodynamic equilibrium conditions to establish the magnetostrictive effect of non-linear constitutive relationship. The constructed model successfully simulates the hysteresis curve and the butterfly curve between the magnetic field and the elastic field, and the experimental results are used to verify the model.