The nonlinear, hysteretic stress-strain characteristic of superelastic shape memory alloys (SMA) results in energy dissipation and therefore in high damping capacities. Due to the nonlinearity the damping capacity strongly depends on the amplitude of the applied excitation. In this work, a rheological non-smooth model is used to describe the principle behavior of superelastic SMA undergoing harmonic displacements. The equivalent mechanical model consists of a spring representing the elastic deformation of the superelastic SMA in austenitic and detwinned martensitic state. A friction element represents the stress plateaus for forward and backward transformation between austenitic and martensitic state. A constant force is applied to the system to generate an offset which shifts the hysteresis to positive force values. Two mechanical stops are implemented to describe the end of the stress plateaus and therefore correspond to the strain differences of the stress levels for forward and backward transformation. Thus, the system behavior is highly amplitude-dependent.
A harmonic approximation of the force generated by the superelastic SMA element during one excitation period is calculated by applying the Harmonic Balance Method to the nonlinear force signal of the rheological model. In this context the Fourier coefficients are calculated by performing a piecewise integration of the force signal. The Integrals are being calculated for each steady interval. The equivalent stiffness and damping coefficients are given for this approximation as functions of excitation amplitude and the system parameters. Based on these results, the damping capacity of a superelastic shape memory element undergoing harmonic displacements is presented using an analytical expression for the damping ratio.