## 3 Model Development and Validation
### Validation of The Finite Element Model  
Four experimental SCS walls with various spacing of connectors carried out in reference [31], were selected to assess the reliability of the FE models developed in this study. The geometry, material details, and test results are given in Table 1.  
The validation of the FE model for the composite walls under axial loading is presented in Figure 8. It is seen that the FE models can reasonably predict the ultimate compressive resistance and the initial stiffness of DSW 1-3. In terms of initial stiffness, the FE results are slightly conservative compared to the experimental test results and the compressive resistance of the four groups of test data increased from 200 kN. This may be justified by the instability of the force sensor of the loading device when the reaction force is marginal. In addition, the initial stiffness of DSW-4 in the FE model was lower than that in the test data due to the lower initial displacement rather than the actual displacements measured by the loading device and loading beam at the commencement of the experiment [45]. Figure 9 shows the  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{\begin{tabular}{c} **Dimension** \\ **(mm\({}^{3}\))** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(\mathbf{t}_{c}\) (mm)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Spacing of** \\ **Connectors (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{**Concrete**} & \multicolumn{2}{c}{**Steel**} & \\ \cline{5-10}  & & & & **\(\mathbf{f}_{\mathbf{c}_{\mathrm{w}}}\)** (MPa)** & \(\mathbf{f}_{y}\) (MPa)** & \(\mathbf{f}_{u}\) (MPa) & \(\mathbf{\varepsilon}_{y}\) (\%) & \(\mathbf{P}_{u}\) (\%) & \(\mathbf{P}_{u}\) (\%) \\ \hline DSW-1 & & & & 150 & 52.4 & & & & 6270 \\ DSW-2 & & & & 100 & 46.8 & & & & 6390 \\ DSW-3 & & & & 75 & 52.4 & & & & 6700 \\ DSW-4 & & & & 35 & 46.8 & & & & 7780 \\ \hline \hline \end{tabular}  
* \(\mathbf{t}_{c}\) = thickness of concrete core; \(\mathbf{t}_{c}\) = thickness of steel plate; \(\varepsilon_{\mathrm{w}}\) denotes the compressive stress of concrete cube; \(\mathbf{f}_{y}\) is the yield stress of steel plates, \(\mathbf{f}_{u}\) is the ultimate tensile stress of steel plates; \(\varepsilon_{y}\) represents the yield strain of steel plates; and \(\mathrm{P}_{u}\) is the ultimate compressive resistance of composite walls.  
\end{table}
Table 1: Dimension and material properties of the SCS walls in reference.  
comparison of the primary failure modes between those from the FE simulations and the test results. The local buckling of the steel plate can be captured for DSW-3 but the deviation of the distribution of buckling are also found. This is because the position of the maximum out-of-plane displacement of steel plates cannot be simulated accurately by the FE model due to the uncertainty of the initial imperfection of steel face plates. As shown in Figure 9c,d, the lateral deformation occurs on the steel plate and the tension fracture in the weld between the steel face plate and the side plate. And the maximum out-of-plane displacement of the steel side plate is 1.1 mm which agrees well with the numerical results [45].  
Figure 8: Experimental and numerical in-plane displacement curves (P-\(\Delta\) curves) of SCS sandwich walls.  
Figure 9: Comparisons of the failure modes between those from the FE simulations and the experimental tests.  
Overall, the FE models can estimate the compressive behavior of the composite wall reasonably. Slight deviations of initial stiffness caused by the measurement method and the distribution of buckling caused by the uncertainty of initial imperfection of steel face plates can be accepted in the numerical analysis.