# Axial Compression Behavior of Steel Angle-Corrugated Steel Plate-Confined Concrete Columns
## 4 Finite Element Analysis
### Material Models  
(1) Core concrete  
The concrete damage plasticity (CDF) model was used to simulate the plastic behavior of concrete for its high accuracy. The Poisson's ratio of core concrete was taken as 0.2, and the initial [PERSON]'s modulus of core concrete was calculated as \(4700f_{c}^{\,0.5}\)[30]. The viscosity  
Figure 11: FE model of SA-CS column.  
parameter was 0.0005. The invariable stress ratio (\(K_{\rm c}\)) and the ratio of the initial equiaxial compressive yield stress to the initial uniaxial compressive yield stress (\(f_{\rm bo}/f_{\rm co}\)) was needed to define the yield surface function [31]. In order to calculate the plastic flow potential of concrete, it was necessary to determine the dilation angle (\(\psi\)) and the flow potential eccentricity (\(e\)). The values of \(\psi\), \(e\), \(f_{\rm bo}/f_{\rm co}\), and \(K_{\rm c}\) were 35\({}^{\circ}\), 0.1, 1.16, and 0.667, respectively.  
The constitutive relationship of confined concrete suggested by [PERSON] [32] et al. was adopted as the compressed stress-strain relationship for the core concrete, as given in Equations (7)-(13). In addition, to determine the tensile behavior of concrete, we adopted the simplified model proposed by [PERSON] [33].  
\[y=\begin{cases}2x-x^{2}&(0\leq x\leq 1)\\ \frac{x}{\beta_{\rm o}(x-1)^{7}+x}&(x>1)\end{cases} \tag{7}\]  
\[x=\varepsilon/\varepsilon_{\rm o} \tag{8}\]  
\[y=\sigma/\sigma_{\rm o} \tag{9}\]  
\[\sigma_{\rm o}={f^{\prime}}_{\rm c} \tag{10}\]  
\[\varepsilon_{\rm o}=(800\xi^{0.2}+1300+12.5{f^{\prime}}_{\rm c})\times 10^{-6} \tag{11}\]  
\[\beta_{\rm o}=\frac{({f^{\prime}}_{\rm c})^{0.1}}{1.2\sqrt{1+\xi}} \tag{12}\]  
\[\eta=1.6+1.5/x \tag{13}\]  
where \(\beta_{\rm o}\) is the adjusting parameter of the stress-strain curve of the descending section of compressive concrete; \(\eta\) is the curve shape coefficient; \(\varepsilon\) and \(\sigma\) are the strain and corresponding stress of concrete; \(\varepsilon_{\rm o}\) and \(\sigma_{\rm o}\) are the peak strain and corresponding stress of concrete; \({f^{\prime}}_{\rm c}\) is the cylinder compressive strength of concrete, which is calculated as 0.8\(f_{\rm co}\); and \(\xi\) is the confinement index, which is calculated as \(f_{\rm y1}A_{\rm s1}/f_{\rm c}A_{\rm c}\), where \(A_{\rm s1}\) is the area of the corrugated steel plate.  
(2) Steel  
As the constitutive steel model has little influence on the bearing capacity of a steel-concrete composite column [34], this research adopts the ideal elastic-plastic model to describe the stress-strain relationship of steel to simplify the calculations [35]. Both the elastic modulus and the yield strength of the steel used measured values, and the Poisson's ratio of steel was taken as 0.3. The model was described as follows:  
\[\sigma_{\rm s}=\begin{cases}E_{\rm s}\varepsilon_{\rm s}&(\varepsilon_{\rm s }\leq\varepsilon_{\rm y})\\ f_{\rm y}+E_{\rm p}(\varepsilon_{\rm s}-\varepsilon_{\rm y})&(\varepsilon_{\rm s }>\varepsilon_{\rm y})\end{cases} \tag{14}\]  
where \(\varepsilon_{\rm s}\) and \(\sigma_{\rm s}\) are the strain and stress of steel, and \(E_{\rm p}\) is taken as 0.01\(E_{\rm s}\).