## 4 Comparing Experimental and Numerical Results
### Verification for the Suggested Analysis Conditions  
In order to verify the analysis conditions presented in the previous section, the shear force according to the horizontal displacement of the analytical model was obtained through numerical simulations at 60A and 70A as well as the hardness of the elastomer 50A. Table 9 shows the material properties of the elastomer according to the shore hardness.  
Figure 14: Correlation of the shear force between the experiment and the FEA when shore hardness of the elastomer is 50A.  
Figure 13: Comparison of shear force-displacement graph between the experiment (mean values of 10 test results) and the numerical simulation (2P M-R model results) at a shore hardness of 50A.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multirow{2}{*}{**Sign**} & \multirow{2}{*}{**Unit**} & \multicolumn{3}{c}{**Values**} \\ \cline{4-6}  & & & **S50A** & **S60A** & **S70A** \\ \hline Mooney–Rivlin & C10 & MPa & 0.302 & 0.382 & 0.474 \\ Constants & C1 & MPa & 0.076 & 0.096 & 0.118 \\ Poisson’s ratio & \(\
u\) & N/A & 0.49 & 0.49 & 0.49 \\ Tensile strength & \(\sigma_{\rm U}\) & MPa & 15.0 & 15.0 & 15.0 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Mechanical properties for an elastomer according to shore hardness.  
The shear forces according to the horizontal displacement for the elastomeric bearing with 3 types of shore hardness (50A, 60A, and 70A) under compression of 392 ton\({}_{\text{f}}\) (corresponding to a pressure of 6 MPa) was found through the numerical simulation (FEA) when the number of elements across an elastomer layer is 3, and is shown in Table 10. The values of Table 10 are plotted in Figure 15 as force-displacement graphs in order to calculate the shear modulus with respect to the shore hardness of an elastomer. The shear forces of the elastomeric bearing are found at the two deformation points (shear strain of 0.27 and 0.58) of each graph in Figure 15, and the shear modulus is calculated using Equation (1), and the values are represented in Table 11.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Displacement** **(mm)**} & \multirow{2}{*}{**Shear Strain**} & \multicolumn{3}{c}{**Shear Forces (Ton\({}_{\text{f}}\))**} \\ \cline{3-5}  & & **S50A** & **S60A** & **S70A** \\ \hline
0 & 0 & 0.0 & 0.0 & 0.0 \\
10 & 0.08 & 7.2 & 9.2 & 11.5 \\
20 & 0.15 & 14.4 & 18.4 & 23.0 \\
30 & 0.23 & 21.6 & 27.7 & 34.5 \\
40 & 0.31 & 28.9 & 36.9 & 46.1 \\
50 & 0.38 & 36.2 & 46.3 & 57.7 \\
60 & 0.46 & 43.5 & 55.7 & 69.4 \\
70 & 0.54 & 50.9 & 65.1 & 81.2 \\
80 & 0.62 & 58.4 & 74.6 & 93.0 \\
90 & 0.69 & 65.9 & 84.2 & 104.9 \\
100 & 0.77 & 73.4 & 93.8 & 116.9 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Shear force and displacement with respect to the shore hardness of an elastomer through the numerical simulation (FEA) when the number of elements across an elastomer layer is 3.  
Figure 15: Shear force-displacement graph with respect to the shore hardness of an elastomer through the numerical simulation (FEA). The thickness of elastomer in this specimen (T\({}_{\text{d}}\)) is 130 mm.  
In Table 11, the shear modulus of the bearing through the numerical simulation (FEA) is 0.731 MPa (when shore hardness is 50A), 0.935 MPa (when 60A), and 1.165 MPa (when 70A). This indicates that the shear modulus of the bearing through the numerical simulation is corresponding to the values in Table 3: EN 1337-3 Annex D: Shear Modulus Comments. This means that numerical simulations by using Mooney-Rivlin constants in Table 10 as mechanical properties and dividing the number of elements across the elastomer layer by 3 are reliable. It shows that the present numerical modeling can reasonably represent the physical model so that it can repeatedly be used for the design.