## 2 Superelastic SMA Materials  
The behavior of typical SMA materials (e.g., nickel-titanium metallic alloys, so called Nitinol), which is plotted as the stress-strain-temperature relationship, is shown in Figure 1. The SMA materials exhibit two crystal phases, _i.e.,_ (a) weaker martensite phase, and (b) stronger austenite phase [19, 22, 23]. These crystal phases account for their unique physical properties known as shape memory effect (SME) and superelastic effect (SE). The SME is easily found at the martensite phase, which mostly appears at a low temperature. Conversely, the SE is easily detected at the austenite phase, which is stable at a high temperature. The SME can be described as a material's ability to regain its original shape upon heating while the SE describes a material's distinct capability to recover its original configuration from large deformation just after the removal of the applied load [22, 23, 24].  
As can be seen in Figure 1, SMA materials exhibit the SME under the temperature below the martensite finishing temperature (_M_). The behavior of martensitic phase SMA materials can accommodate a considerable amount of plastic strain arising due to the low stress plateau, and then display a large value for residual strain upon unloading. Once SMA materials are heated above the austenite finishing temperature _(A)_, they begin to recover their original shape from residual strain. It is because the phase transformation from weak detwinned martensite to strong body-centered austenite occurs during heat treatment. The SMA materials go back to twinned martensite upon cooling, thereby completing one cycle of phase transformation owing to the SME [22]. On the other hand, superelastic  
Figure 1: Behavior of superelastic shape memory alloy (SMA) materials according to phase transformation.  
behavior, referred to as a flag-shape hysteretic loop having almost zero-residual strain, appears at a temperature greater than _A/._ The austenitic phase SMAs subjected to a range of up to 8% strain are capable of fully recovering their original shape [23]. The austenitic phase SMAs at the flag-shaped hysteresis curve exhibit higher stress-leveled slip plateaus than the martensitic phase SMAs. The phase transformation converted from austenite to stress-induced martensite takes place along the path of the slip plateau. Even when constant temperatures are maintained, the stress-induced reverse transformation back to the austenite phase that causes the SE occurs upon unloading.  
Superelastic SMAs, owing to their ideal properties, are particularly good examples of promising smart materials in the engineering field. The damper systems retrofitted with superelastic SMAs are expected to benefit from recentering capability, guaranteed by the SE and supplemental damping attributed to energy dissipation. The stress slip plateau in the flag-shape hysteresis helps to limit force transmission at the intermediate strain level [25,26]. Furthermore, these materials include excellent corrosion resistance as well as outstanding fatigue strength [22]. Once superelastic SMA bending bars are installed to be integrated with steel slit dampers, we expect that the equipped structures will make the best use of SMA material's unique properties. In this paper, the effectiveness of the damper system retrofitted with such seismic restrainers will be investigated primarily through nonlinear 3D FE analyses cyclically tested.