On the influence of the constitutive modeling on the nonlinear dynamic response of shape memory alloys oscillators

Shape Memory Alloys (SMA) are, nowadays, well known materials with widespread applications in several fields. Many applications are based on Shape Memory Devices (SMD) that combine various elements of SMA to obtain an optimized response. In many cases, applications of SMD take advantage of the nonlinear dynamic response. Since SMA exhibit a complex thermomechanical behavior the topic of their constitutive modeling attracted the interest of several authors who studied the nonlinear dynamics of SMA oscillators, by using different constitutive models. For example, in [1] and [2] different types of internal variable models were used, whereas the works [3] and [4] adopted simpler polynomial ones. Internal variable models are richer and can take into account most of the complex features of the SMA, on the contrary, polynomial models are strongly approximate, being based on a Falk-type free energy that gives rise to a non-hysteretic non-monotonic force-displacement curve. While the two types of models give completely different results in the force-displacement-temperature space, in nonlinear dynamics one is often interested in more global information like, for example, the maximum displacement over a trajectory. Therefore it is interesting to investigate how much the fine details of the constitutive modeling actually influence the global dynamical information. To this end, in this work a comparison between different constitutive assumptions for the modeling of the restoring force provided by SMD is carried out. The dynamic response of the corresponding oscillators is discussed through the analysis of single trajectories in different conditions as well as the numerical construction of frequency-response curves. The results show that, in some particular situations like for example when the pseudolastic loops do not involve the second elastic branch, the essence of the overall dynamic response can be captured also with simplified models. However, in all other conditions, the proper modeling of the hysteretic behavior and all of the peculiar functional properties of SMD have to be taken into account by a suitable model.