## 6 Modeling Verifications  
The FE analysis results are compared with the experimental test results for the purpose of verifying the adequacy of FE modeling. The results were obtained from the experimental tests performed on steel slit dampers without seismic restrainers, which were subjected to cyclic shear loads. The applied force _versus_ displacement curves for slit damper models (\(P_{\mathrm{slit}}\)_vs_. \(\Delta_{\mathrm{slit}}\)) is presented in Figure 9. The instrumentation for applied force and displacement measurement is illustrated in Figure 4. The experimental tests were conducted until slit damper specimens completely failed by fracture while the FE analyses were carried out with the same load history as the comparable experimental test. All steel slit damper specimens are able to dissipate a considerable amount of yielding energy even under small displacement loading owing to the bending mechanism at the slender strips. Furthermore, the characteristics of the used base steel materials enable these damper systems to behave well with gradual strain hardening and Bauschinger behavior, as can be seen in Figure 9. In spite of stable energy dissipation, the amount of permanent deformation augments as the number of loading cycles simultaneously increases. The ratio of strip depth to strip width (\(b\)/\(l_{\mathrm{o}}\)), which is a significant parameter used to classify the specimen, has an influence on ultimate strength at the resulting curve. The SL1 specimen, which has the smallest \(b\)/\(l_{\mathrm{o}}\) ratio, only reaches the ultimate strength of approximately 21.5 kN at the displacement of 17.5 mm, while the SL6 specimen designed with the largest \(b\)/\(l_{\mathrm{o}}\) ratio gets to as much as 32.5 kN strength at the displacement of 10 mm. Rapid strength degradation is observed at the behavior of the SL6 specimen due to the shortest strip depth after reaching ultimate strength. On the other hand, the SL1 specimen designed with relatively long strip depth (\(l_{\mathrm{o}}=97\) mm) arrives at the ultimate displacement without strength degradation, meaning that this model possess excellent ductility. In general, both cyclic curves compared to each other show good agreements in terms of initial stiffness, yield force, post-yielding envelope, unloading stiffness, reloading stiffness, ultimate force, permanent deformation, and even pinching points. The FE models also exhibit symmetric-shape hysteresis loops with stable energy dissipation before strength degradation occurs. These good agreements between experimental results and analysis results indicate that FE models provided herein are appropriate for  
Figure 8: Simulated stress-strain curve for the super-elastic SMA material, (**a**): Experimental Curve; (**b**): Simulated Curve. estimating the behavior of the slit dampers cyclically tested. The effect of the design parameter as well as that of the used base material can be examined through the FE analysis results, simultaneously. Figure 9: _Cont._  
For more detailed examination, comparisons of experimental results (Exp.) to FE analysis results (Anal.) are summarized in Table 2. The resulting findings, such as initial stiffnesses (\(K_{\text{slit}}\)), yield forces (\(P_{\text{slit,y}}\)), ultimate forces (\(P_{\text{slit,max}}\)), yield displacements (\(\Delta_{\text{slit,y}}\)), and ultimate displacements (\(\Delta_{\text{slit,max}}\)) for individual slit damper specimens are listed in this table. The initial stiffnesses are obtained from yield force divided by yield displacement as follows:  
\[K_{\text{slit}}=\frac{P_{\text{slit,y}}}{\Delta_{\text{slit,y}}} \tag{3}\]  
The initial stiffnesses can be theoretically defined with an assumption that individual strips are considered to be fully constrained beams at both end supports, and thus determined as follows:  
\[K=n\frac{12E_{\text{s}}I}{l_{0}^{3}}=n\,\frac{E_{\text{s}}tb^{3}}{l_{0}^{3}} \tag{4}\]  
where \(n\) and \(E_{\text{s}}\) indicate the number of strips and the elastic modulus of Gr. 50 steel materials, respectively.