Ferromagnetic shape memory alloys (FSMAs) allow the development of novel kinds of actuators, which can be controlled by a combination of applied stress, temperature, and magnetic field. For simulation and optimization of such actuators having an arbitrary shape, it is important to develop a validated model and an appropriate tool for field simulation such as the finite element method (FEM). The main goal of the present study is to develop a free energy model, which captures the main effects of variant reorientation on the strain and magnetization, and to implement the model in a FEM routine, which takes into account both the actuator geometry and the complex thermo-magneto-mechanical coupling of the material. A free energy function is constructed, which couples strain and magnetic moments in the FSMA material. The associated Gibbs function is used to calculate time-dependent transition probabilities between martensite variants in a magnetic field under applied stress. By keeping track of the variant fractions, the evolution of strain and magnetization is determined. The simulation model is applied to a beam actuator to verify magnetic field-dependent strain and magnetization characteristics. The influence of a coupling term between strain and magnetic anisotropy on these characteristics is discussed.

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