This paper presents a new phenomenological model for magnetic shape memory (MSM) alloy actuators. The model was implemented as a lumped element for multi-domain network models using the Modelica language. These network models are rapidly computed and are therefore well suited for MSM-based actuator design and optimization. The proposed MSM model accounts for the 2-D hysteresis of the magnetic field-induced strain as a function of both the applied magnetic flux density and the compressive stress. An extended Tellinen hysteresis formulation was utilized to compute the mechanical strain of the MSM material from measured upper and lower limiting hysteresis surfaces. Two alternative approaches for the computation of the lumped element have been implemented. The first method uses hyperbolic shape functions to approximate the limiting hysteresis surfaces and offers a good balance of simulation accuracy, numerical stability, computational speed, and ease of parameter identification. The second method uses 2-D lookup tables for direct interpolation of the measured limiting hysteresis surfaces, which leads to higher accuracy. Finally, a test case having simultaneously varying compressive stress and magnetic flux density was utilized to experimentally validate both methods. Sufficient agreement between the simulated and measured strain of the sample was observed.Index Terms-Hysteresis, lumped network model, magnetic shape memory (MSM) alloy, multi-domain.

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A novel lumped-element modeling approach for magnetic shape memory alloys is presented. Building on concepts borrowed from rate-independent plasticity, the model describes the magnetic and magneto-mechanical behavior of a magnetic shape memory component subjected to a particular load case in a thermodynamically consistent way. The approach remedies the common issues of existing models regarding the representation of inner hysteresis loops and small-signal behavior. The model is parametrized in terms of a small number of parameters, which can be determined from single variant magnetic curves and mechanical first order reversal curves at constant magnetic input. The results indicate that the model predicts the magnetic and magneto-mechanical behavior with sufficient accuracy, which makes it appropriate for system design.