# Experimental Investigation of a Device to Restrain the Horizontal Sliding of U-FREIs
## 8 Test Results and Observations
### Shear Test Results
#### 8.2.2 Quasi-Static Shear Test  
Figure 14 shows the load-displacement curves of all the performed static shear tests. As stated above, the Q specimens were subjected only to the tests without constraint and  
Figure 12: Diagrams relevant to bond failure: (**a**) Q specimens under 0.375 MPa; (**b**) Q specimens under 0.25 MPa; (**c**) B specimens under 0.5 MPa.  
Figure 13: Damage to the (**a**) hooks and (**b**) elastomer.  
with one constraint, because during the previous bond test, one of the external elastomer layers was damaged by the metal hooks. Hence, for the quasi-static shear test, the Q specimens were constrained only on the surface that had not been damaged. Although these damages also occurred in the B specimens during the bond test, quasi-static shear tests with two constraints were also carried out on these specimens. In Figure 14, it can be observed that, in all cases, the isolator behavior stabilized at the third cycle in terms of both the wideness of the cycle, i.e., dissipated energy, and maximum force, after having undergone the Mullins effect. A residual displacement is observed at the end of every cycle due to the viscous-elastic properties of the elastomer. No further damages were observed in the specimens after performing the quasi-static shear tests.  
Figure 14: Force–displacement curves of quasi-static shear test: (**a**) without constraint; (**b**) with constraint on one contact surface; (**c**) with constraint on both contact surfaces.  
Considering the configuration without constraint (Figure 14a), the Q specimens performed wider loading cycles than the B specimens, thus showing a greater capacity for dissipating energy. This is due to the different elastomer type used to make the specimens, which was high-damping natural rubber for the Q specimens and low-damping neoprene for the B specimens.  
In the graphs, no horizontal strokes or instantaneous force decreases are observed, which suggests breakage phenomena, such as delamination of the internal layers, or sliding of the isolators with respect to the contact surfaces.  
Table 4 reports the secant stiffness values, \(K_{sec}\), calculated in the third loading cycle according to Equation (3) for all the tested specimens and configurations, apart from Q-1 specimens. For these specimens, it was not possible to determine the F\({}_{0.27t_{e}}\) value due to the residual displacement of the third cycle, which was greater than 0.27\(t_{e}\). For the B specimens, Table 4 also reports the \(K_{sec}\) variations between the test configuration with one constraint and configuration with no constraint (\(\Delta\)K\({}_{\text{sec}}\)-0), and between two constraints and one constraint (\(\Delta\)K\({}_{\text{sec}}\)-1). From these variations, which were lower than 6%, it is observed that the introduction of the constraint system did not substantially affect the secant stiffness, neither for the one-surface configuration nor for that of the two surfaces (see also Figure 15).  
For the Q specimens, by simply calculating the secant stiffness between the point at zero force of the ascending branch and the point at maximum force (see Figure 15), the values of 1.25 kN/mm and 1.13 kN/mm were determined for the specimens with no constraint and with one constraint, respectively. In this case, the difference was about 9%.  
The data in Table 4 are shown in graph form in Figure 16. From this figure, it can also be stressed that Q-0 specimens are stiffer than B-0 specimens.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(K_{sec}\) (kN/mm) & \(\Delta\)K\({}_{sec}\)-0 (\%) & \(\Delta\)K\({}_{sec}\)-1 (\%) \\ \hline Q-0 & 1.20 & & \\ Q-1 & - & & \\ B-0 & 1.03 & & \\ B-1 & 1.08 & 4.85 & \\ B-2 & 1.02 & \(-5.56\) & \(-0.97\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: K\({}_{sec}\) values and percentage variations in the presence of constraints.  
Figure 15: Comparison of cycle III of the quasi-static shear test among different constraint configurations.