## 2 Verification with Finite Element Model
### Constitutive Relation  
In this study, the steel pipe finite element model is simulated with the various isotropic elastic-plastic models provided by ABAQUS, and the stress-strain is simulated with the ideal elastic-plastic model, as shown in Figure 3. The constitutive relationship expression is as follows:  
\[\sigma=\left\{\begin{array}{c}E_{\mathrm{s}}\xi,\varepsilon\leq\varepsilon_{ \mathrm{y}}\\ f_{\mathrm{y}}\,\varepsilon>\varepsilon_{\mathrm{y}}\end{array}\right\} \tag{1}\]  
where:  
\(E_{\mathrm{s}}\)--elastic modulus of steel;  
\(f_{\mathrm{y}},\ \varepsilon_{\mathrm{y}}\)--yield strength and corresponding yield strain of steel;  
\(\sigma,\ \varepsilon\)--steel stress and corresponding strain.  
The elastic modulus of square steel pipe is 2.02 \(\times\) 10\({}^{5}\) MPa, [PERSON]'s ratio is 0.25, and the yield strength is 247 MPa.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Steel** & \(f_{\mathrm{y}}\)**/MPa** & \(f_{\mathrm{z}}\)**/MPa** & \(E_{\mathrm{s}}\)**/10\({}^{5}\) MPa** \\ \hline Q195 & 201 & 284 & 2.01 \\ Q235 & 247 & 321 & 2.02 \\ Q345 & 363 & 542 & 1.96 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of steel.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Concrete** & \(f_{\mathrm{c}}\)**/MPa** & \(f_{\mathrm{c}}\)**/MPa** & \(E_{\mathrm{c}}\)**/10\({}^{4}\) MPa** \\ \hline C40 & 26.8 & 18.4 & 2.26 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties of concrete.  
Figure 2: Concrete-filled steel tubular specimen. (**a**) Before test loading. (**b**) Peak bearing capacity. (**c**) After test loading.  
The concrete damage plasticity model (CDP) is based on the principles of damage mechanics and considers the effects of damage on concrete materials under monotonic loading, reciprocal loading and dynamic analysis. The CDP is based on the principles of damage mechanics and considers the effects of damage generation, accumulation and evolution on the material under monotonic loading, reciprocal loading and dynamic analysis of loading conditions. It is suitable for simulating the stiffness degradation of the material due to damage and the mechanical behavior of stiffness recovery during reverse loading. It is suitable for modelling the mechanical behavior of the material in terms of stiffness degradation due to damage and stiffness recovery during reverse loading. Based on this, the CDP model is used to establish the intrinsic structure relationship for concrete sections. The concrete plastic damage parameters are shown in Table 3.  
Core concrete in steel pipes under axial compression and other external loads is a typical confined concrete under three-way compression. The constitutive relation of section concrete in this paper adopts the restraint concrete constitutive model proposed by [PERSON], [PERSON] [17], and its stress-strain curve is shown in Figure 4.  
Figure 4: Stress–strain curves of concrete.  
Figure 3: Stress–strain curves of steel.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Concrete**} & \multirow{2}{*}{\begin{tabular}{c} **Expansion** \\ **Angle** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Flow Potential** \\ **Bias** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Stress Ratio** \\ **Stress Ratio** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Invariant** \\ **Stress Ratio** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Viscosity** \\ **Coefficient** \\ \end{tabular} } \\ \hline C40 & 35 & 0.1 & 1.16 & 0.667 & 0.0005 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Plastic damage parameters for concrete.