# Behaviour Investigation of SMA-Equipped Bar Hysteretic Dampers Using Machine Learning Techniques
## 2 Shape Memory Alloys  
Shape memory alloys (SMAs) are considered smart and innovative materials discovered as early as 1932 and, in 1960, were manufactured from nickel and titanium [78] to exhibit better behaviour than any other element used in memory alloys. These polymorphic materials are composed of crystalline or chemical phases. SMAs are capable of enduring large stresses without causing residual strains, and it is efficient in dissipating energy [79]. In shape memory alloys, the prevailing crystalline phase is dependent on the temperature and stress. Austenite and martensite are the two crystalline phases of SMAs. Austenite and martensite phases are stable at high and low temperatures and low and high stresses, respectively [80]. Therefore, these two phases could be transformed into each other through a heating process or by applying mechanical forces. SMAs exhibit different macroscopic behaviour during the transition from one phase to another. There are certain characteristics that distinguish SMAs from other alloys and metals, specifically, shape memory and superelasticity features. SMAs' mechanical behaviour under different levels of stress and strain and various temperatures is shown in Figure 1. A shape memory feature is present in SMAs at temperatures below the austenite-transformation-to-martensitic phase during cooling, \(M_{f}\), and the superelasticity feature is created when the temperature is above the finish temperature of the martensite-transformation-to-austenite phase during heating, \(A_{f}\)[79]. At temperatures below \(M_{f}\) and in the martensitic phase, SMAs deform under stress. By load removal, the alloy could not return to its original shape and would experience residual strains. In this case, named the one-way shape memory feature, the martensitic phase is still dominant in SMAs.  
In a one-way shape memory feature, just heating and cooling processes could convert the martensite and austenitic phases into one another without stress being applied. This case in which SMAs could remember their different shapes at high and low temperatures is named the two-way shape memory feature. SMAs with two-way shape memory characteristics are among the few that exist and are utilised in temperature-sensitive actuators and reversible fasteners in medical research fields [78; 80]. By applying stresses, the austenitic phase of SMAs would be transformed into the martensitic phase at a higher temperature than \(A_{f}\) and lower than \(M_{d}\) (a higher temperature than \(A_{f}\), at which the alloy has an elasto-plastic feature). As shown in Figure 1, unloading in this situation leads to an unstable martensitic phase, which undergoes an inverse transformation that leads SMAs to return to their original state with no residual strain. This feature is named superelasticity and is utilised in many engineering fields [79].  
Researchers used this smart material in many different fields due to austenitic to martensitic transformation, resulting in shape memory and superelasticity properties. The superelasticity property of SMAs is used in this study to improve the seismic behaviour of bar hysteretic dampers utilising the stress-strain model introduced by [PERSON] and [PERSON] [81] and also used in finite element SeismoStruct software [82]. As presented in Figure 2, the most important parameters in this model are \(\sigma_{f}^{EA}\) (stresses relating to the beginning transformation of the austenitic into the martensitic phase), \(\sigma_{s}^{SA}\) (stresses linked to the end of the austenitic phase into the martensitic phase transformation), \(\sigma_{s}^{AS}\) (stresses related to the beginning of unloading step), \(\sigma_{f}^{AS}\) (stresses relating to the ending of the unloading step), \(\varepsilon_{l}\) (strain equivalent at the unloading step) and \(E_{SMA}\) (elastic modulus in the austenitic phase) [81].  
Figure 1: Shape memory and superelasticity features of SMAs [79].