The physical properties of Shape Memory Alloys (SMA), useful in damping effects of scarce events as quakes, are studied for Cu-based alloys (CuAlBe) and partially for NiTi in the appropriate time scale. The evaluation of the deformation (e) in the hysteresis cycle and in their internal loops, against the thermodynamic forces, i.e. the external stress (σ ext ) and temperature (T) is performed. The main goal for the applicability of the alloys centers in reliable behavior after several years of inactivity. The alloy require a minimal transformation temperature change and, also, within a reduced transient time to ensure that the material always remain inside the thermoelastic window (full parent phase recovery at zero stress and without permanent deformation at maximal stress). The macroscopic behavior associated with the Clausius-Clapeyron equation, the material fatigue and the local temperature changes, produced by latent heat and by frictional contributions, are critically visualized. The microscopic phenomena related with the transient after quenched effect, the evolution in the region of phase coexistence and the long time seasonal actions in parent phase are, also, evaluated.