Chaos robustness and strength in thermomechanical shape memory oscillators. Part I: a predictive theoretical framework for the pseudoelastic behavior

In this two-part paper the problem of evaluating robustness and strength of chaos in thermomechanically-based Shape Memory Oscillators (SMO) is addressed. In the first part, a theoretical analysis of the main features of the pseudoelastic loops exhibited by the underlying Shape Memory Devices (SMD) is accomplished with the aim to establish a predictive framework for accompanying numerical investigations. The analysis is based on the evaluation of suitable synthetic indicators of the SMD behavior that can be computed from the model parameters before the computation of SMO actual trajectories, and provide information about the hysteresis loops and their dependence on temperature variations. By means of such indicators, a detailed analysis of the influence of thermomechanical coupling on the rate-dependent mechanical response is presented. It is shown that a careful interpretation of the synthetic indicators permits to obtain a reasonable estimation of the influence of various model parameters on the hysteresis loop area and slopes of the pseudoelastic plateaus, that are the main global aspects influencing the occurrence of chaotic responses. In the second part, the theoretical predictions based on the synthetic indicators will be exploited to interpret the results of a systematic numerical investigation based on an enhanced version of the Method of Wandering Trajectories