In this paper, a coupled FEM-BEM method is applied to simulate the magneto-mechanical behavior of a single-crystalline Ni-Mn-Ga sample. First, based on some kinematic and constitutive assumptions, the governing system for modeling the response of the Ni-Mn-Ga sample is formulated, which is composed of the magnetic and mechanical field equations, the evolution laws of the internal variables and the twin interface movement criteria. To solve the governing system, an iterative numerical algorithm is proposed. Especially, a coupled FEM-BEM method is adopted in the algorithm to tackle the magnetic field equation. By using this method, one doesn’t need to consider the distribution of the demagnetization field in the surrounding space, thus the number of elements can be reduced significantly. To show the efficiency of the numerical algorithm, some typical examples are studied. It can be found that the numerical results obtained from the coupled FEM-BEM method and the conventional FEM method are in good agreement with each other. The numerical algorithm proposed in the current work would be helpful for the design of novel smart devices made of Ni-Mn-Ga alloys.

本文采用耦合有限元-边界元方法来模拟单晶Ni-Mn-Ga样品的磁-机械行为。首先，基于一些运动学和本构假设，建立了用于建模Ni-Mn-Ga样品响应的控制系统，该系统由磁场和机械场方程，内部变量的演化规律和孪生界面组成。运动标准。为了解决控制系统问题，提出了一种迭代数值算法。特别是，该算法采用耦合有限元-边界元法求解磁场方程。通过使用这种方法，无需考虑退磁场在周围空间中的分布，因此可以显着减少元素数量。为了显示数值算法的效率，研究了一些典型的例子。可以发现，通过耦合有限元-边界元方法和常规有限元方法获得的数值结果相互吻合。当前工作中提出的数值算法将有助于设计由Ni-Mn-Ga合金制成的新型智能设备。