## 3 Model Development and Validation
### Validation of the Finite Element Model
#### 3.3.2 The Simulation of the Double-Step Performance of the HESs  
The detailed geometric parameters are listed in Table 1, Table 2 and Figure 7. The monotonic behavior of specimen HES1 is simulated and the results are shown in Figure 7 and its displacement threshold is set as 3 mm. When the shear displacement is applied to 0.24 mm (the drift ratio = 0.12/100), the steel plate in the ED zone begins to yield and the yielding area gradually enlarges from the two ends of the steel plate to the middle part as shown in Figure 8a. With the increment to 3 mm (the drift ratio \(\theta\) = 1.5/100), the steel plate totally comes into plastic and the shear strength of HES1 comes to the end of its first step, as shown in Figures 8b and 9a. With the development of deformation, the SL zone begin to work and when the horizontal displacement is up to 3.8 mm (the drift ratio = 1.9/100), the middle part of functional bolts yields, the shear stiffness lifting plate is almost in elastic with slight stress concentration at the bolt holes as shown in Figure 8c,d. Finally, the full section of the functional bolts come into plastic and the shear stiffness lifting plate locally yields, as shown in Figure 8e,f. The top and bottom boundaries utilized thick steel plates to simulate the connection to shear walls. When the HES is employed in steel composite shear wall system [42] and steel-damping-concrete composite wall sytems [43] the high strength bolt connection is available. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{8}{c}{**The Typical Dimensions for All HES Specimens (mm)**} \\ \cline{2-13}  & **b\({}_{\text{w}}\)** & **h\({}_{\text{w}}\)** & **t\({}_{\text{w}}\)** & **b\({}_{\text{t}}\)** & **h\({}_{\text{t}}\)** & **t\({}_{\text{t}}\)** & **R\({}_{\text{1}}\)** & **R\({}_{\text{2}}\)** & **D\({}_{(\text{R1}\text{- R2})}\)** & **R\({}_{\text{3}}\)** & **b\({}_{\text{w1}}\)** & **h\({}_{\text{w1}}\)** & **b\({}_{\text{w2}}\)** & **h\({}_{\text{w2}}\)** \\ \hline HES1 & 200 & 200 & 10 & 200 & 330 & 16 & 11 & 8 & 3 & - & - & - & - \\ HES2 & 200 & 200 & 10 & 200 & 330 & 16 & 11 & 8 & 3 & - & 50 & 100 & - & - \\ HES3 & 200 & 200 & 12 & 200 & 330 & 16 & 11 & 8 & 3 & - & 50 & 100 & - & - \\ HES4 & 200 & 200 & 10 & 200 & 330 & 16 & 10 & 8 & 2 & - & - & - & - & - \\ HES5 & 200 & 200 & 10 & 200 & 330 & 16 & 11 & 8 & 5 & - & - & - & - & - \\ HES6 & 200 & 200 & 10 & 200 & 330 & 16 & 11 & 8 & 3 & - & - & - & 50 & 50 \\ HES7 & 200 & 200 & 10 & 200 & 330 & 16 & 11 & 8 & 3 & 50 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific dimensions for HES specimens. Figure 6: The validation of the finite element modelling method. (**a**) Finite element model, (**b**) tested failure mode, (**c**) simulated failure mode, (**d**) hysteresis curves. The double-step force-displacement curve of HES1 is depicted in Figure 9a and the typical double-step working mechanism of the HESs is shown in Figure 9b. The performance of the HES can be observed with four stages including the completely elastic stage, ED plastic stage, SL elastic stage and functional bolts plastic stage. In the completely elastic stage (the OA line in Figure 9a), steel plates in ED are in elastic and the initial shear stiffness is K1 = 525.19 kN/mm. When coming to the ED plastic stage (the AB line), the input seismic energy is mainly dissipated by the plastic deformation. From point B to point C (the SL elastic stage), the SL zone is almost in elastic and the HES restores the bearing  
Figure 8: The validation of the finite element modelling method. **(a)** The stress distribution of ED zone (\(\theta=0.12\%\)), **(b)** the stress distribution of ED zone (\(\theta=1.5\%\)), **(c)** the stress distribution of SL zone (\(\theta=1.9\%\)), **(d)** the stress distribution of functional bolts (\(\theta=1.9\%\)), **(e)** the stress distribution of SL zone(\(\theta=5\%\)), **(f)** the stress distribution of functional bolts (\(\theta=5\%\)). Figure 7: The detailed dimensions of HES specimens.