Abstract In this paper, we introduce a modeling work on the variant reorientation in a single-crystalline Ni–Mn-Ga sample induced by a quasi-static rotating magnetic field. First, some constitutive assumptions are proposed for the variant state distribution, the effective magnetization and the elastic energy density of Ni–Mn-Ga alloys. Then, the total energy functional for a Ni–Mn-Ga sample subject to coupled magneto-mechanical loads is formulated. Through a variational approach, the governing equation system of the model can be formulated, which is composed of the magnetic and mechanical field equations, the evolution laws of some internal variables and the twin interface movement criteria. An efficient numerical scheme is adopted to solve the governing system. With the obtained numerical solutions, we first analyze the evolution properties of the configurational force on the twin interfaces. Especially, the effects of the application directions of magnetic fields on the configurational force are investigated. The influences of the different energy terms on the configurational force are also analyzed. Based on these results, we further conduct numerical simulations on the magneto-mechanical behavior of the Ni–Mn-Ga sample subject to a quasi-static rotating magnetic field. The predicted global responses of the Ni–Mn-Ga sample show good consistency with the experimental result. The configurations of the sample and the distributions of some important physical quantities in the sample during the different loading stages can also be described. Furthermore, by considering the properties of the configurational forces, the underlying mechanisms responsible for the rotating field-induced variant reorientations can be revealed.

中文翻译：

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准静态旋转磁场引起的单晶 Ni-Mn-Ga 样品的变体重新定向：基于构型力的机理分析

摘要 在本文中，我们介绍了由准静态旋转磁场引起的单晶 Ni-Mn-Ga 样品中变体重新定向的建模工作。首先，对 Ni-Mn-Ga 合金的变态分布、有效磁化强度和弹性能量密度提出了一些本构假设。然后，公式化了受到耦合磁机械负载的 Ni-Mn-Ga 样品的总能量泛函。通过变分方法，可以建立模型的控制方程组，该方程组由磁场和机械场方程、一些内部变量的演化规律和双界面运动准则组成。采用一种有效的数值方案来求解控制系统。用得到的数值解，我们首先分析了孪晶界面上构型力的演化特性。特别是，研究了磁场的施加方向对构型力的影响。还分析了不同能量项对构型力的影响。基于这些结果，我们进一步对 Ni-Mn-Ga 样品在准静态旋转磁场下的磁力学行为进行了数值模拟。Ni-Mn-Ga 样品的预测全局响应与实验结果具有良好的一致性。还可以描述样品在不同加载阶段的构型和一些重要物理量在样品中的分布。此外，通过考虑构型力的特性，