Smart materials, such as thermal or magnetic shape memory alloys, provide interesting characteristics for new solid state actuators. However, their behavior is highly nonlinear and determined by strong hysteresis effects. This complex behavior must be adequately considered in simulation models which can be applied for efficient actuator design and optimization. We present a new phenomenological lumped element model for magnetic shape memory alloys (MSM). The model takes into account the two-dimensional hysteresis of the magnetic field induced strain as a function of both the compressive stress and the magnetic flux density. It is implemented in Modelica. The model bases on measured limiting hysteresis surfaces which are material specific. An extended Tellinen hysteresis modeling approach is used to calculate inner hysteresis trajectories in between the limiting surfaces. The developed model provides sufficient accuracy with low computational effort compared to finite element models. Thus, it is well suited for system design and optimization based on network models. This is demonstrated with exemplary models of MSM based actuators. System models and simulation results are shown and evaluated for different topologies.
