# Behaviour Investigation of SMA-Equipped Bar Hysteretic Dampers Using Machine Learning Techniques
## 4 Experimental Specimens and Numerical Models
### Numerical Models  
In this paper, considering the experimental study conducted by [PERSON] et al. [57], the numerical models of isolation systems and SBHDs were generated in the SeismoStruct software to determine whether the software could achieve the expected results [82]. In these models, the same cyclic loading pattern presented in Figure 7 was applied, and using the software link element, the rubber isolator was simulated by a bilinear spring. On the other hand, since this study seeks the influence of geometrical parameters on the cyclic behaviour of bar hysteretic dampers, according to Figure 8, the steel bars were precisely modelled by SeismoStruct software. Figure 8 shows that steel bars are integrated into the isolation system by passing through orifices of a loading plate (_Loading Plate_) subjected to cyclic loads. According to the experimental test setup, each free ends of the bars are restrained by two plates (_Bearing Plates_) from lateral movement and rotation (from the experiment supports). Based on the mechanical characteristics of steel materials reported in [PERSON] et al. [57] experiments, with an elastic modulus of 200 GPa, yield stress of 250 MPa, and yield strain of 0.002, the same mechanical properties of steel materials were introduced into the software for use in the numerical model. The responses of the numerical models under cyclic loading were obtained by evaluating support reactions and mid-length displacements of bars, and the integrated results were presented as hysteresis curves. The experimental and numerical hysteretic curves shown in Figure 9 compare the bare rubber isolator and those isolators equipped by SBHDs. Figure 9 illustrates the hysteresis curves of the bare rubber isolators, and those equipped with SBHDs obtained from numerical models are fitted with the corresponding experimental results. Consequently, using SeismoStruct software and the mechanism utilised to generate this numerical model is reliable to conduct geometrical investigations. Figure 8: Numerical model of rubber isolator equipped by SBHDs in SeismoStruct software. In this paper, to compare the cyclic behaviour of utilising SMA bars as an alternative of steel bars in hysteretic dampers, the proposed SBHD sample by [PERSON] et al. (2016) includes 6 steel bars with 38 mm diameter and 1.5 m long, which was selected as the reference. Then, all SMA-BHD numerical models were constructed by considering equal elastic stiffness (\(K_{e}\)) as presented in Equation (2). \[K_{e}\_SMA=K_{e}\_STEEL \tag{2}\]  
Based on Equation (3), the elastic stiffness of bar hysteretic dampers could be calculated by their corresponding geometrical and mechanical properties. \[K_{e}\_Eqs.=\frac{3N\pi D^{4}E}{L^{3}} \tag{3}\]  
In Equation (3), \(N\), \(D\), and \(L\), respectively, represent the number, diameter, and length of bars, and \(E\) indicates the elasticity modulus of the utilised materials in bar hysteretic damper. In this paper, as reported in Table 1, based on an experimental study ([PERSON] et al., 2016), three different sets of SMA materials (Figure 2) were considered to be compared with the corresponding steel material used in bar hysteretic dampers. For each of Set 1 to Set 3 material, one to ten (1, 2, 3, 4, 5, 6, 7, 8, 9, and 10) numbers of SMA bars (\(N\)) with cross sections ranging from 10 to 50 mm (\(\Phi\)10, \(\Phi\)12, \(\Phi\)14, \(\Phi\)16, \(\Phi\)18, \(\Phi\)20, \(\Phi\)22, \(\Phi\)24, \(\Phi\)26, \(\Phi\)28, \(\Phi\)30, \(\Phi\)32, \(\Phi\)34, \(\Phi\)36, \(\Phi\)38, \(\Phi\)40, \(\Phi\)42, \(\Phi\)44, \(\Phi\)46, \(\Phi\)48, and \(\Phi\)50 rebar) in diameter (\(D\)) were selected. Then, by considering equal \(K_{e}\) for SMA-BHDs and corresponding reference experimental SBHD, the equivalent length (\(L\)) of SMA bars could be obtained by Equations (2) and (3). SeismoStruct software ([PERSON] et al., 2016) was utilised to build the numerical models to investigate the influence of different geometric parameters and mechanical features on SMA-BHDs' cyclic behaviour.