## 2 Finite Element Model of Prefabricated Modular RCS Composite Node
### Overview of Node Design
#### 2.1.2 The Constitutive Relationship of Steel, Bolt Material and Concrete  
In this paper, the elastic-plastic behavior of steel is defined in ABAQUS as follows: during the small deformation loading stage, it exhibits linear elasticity; after exceeding the yield point, stiffness decreases, and strain is divided into elastic and plastic components. At the end of unloading, elastic strain disappears, and plastic strain is irrecoverable; when reloading, the yield stress increases. The constitutive relations for the steel columns and beams are modeled using the double broken-line model based on experimental data. The Mises yield criterion and the dynamic strengthening criterion are applied [19], assuming that the Young's modulus is the same in both the tension and compression directions, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Steel** & \(f_{y}\)/**MPa** & \(f_{u}\)/MPa** & \(E_{s}\)/MPa** \\ \hline Steel beam & 305.8 & 431.3 & 2.1 \(\times\) 105 \\ Load-bearing steel plate & 271.8 & 428.0 & 2.0 \(\times\) 105 \\ HPB235 & 289.5 & 445.6 & 2.0 \(\times\) 105 \\ HRB335 & 383.1 & 558.2 & 2.0 \(\times\) 105 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of steel materials. and that the stress-strain curve is linear. This setting effectively simulates the mechanical behavior of steel in different loading stages and provides reliable theoretical help for the subsequent analysis. In the figure, \(E_{s}\) represents the Young's modulus of the steel and high-strength bolts, with a Poisson's ratio of 0.3. \(f_{y}\) denotes the yield strength of the steel. \(\alpha E_{s}\) refers to the modulus in the strengthening phase of the steel, \(f_{u}\) indicates the tensile strength of the steel and \(\varepsilon_{u}\) represents the tensile strength strain, \(\alpha=0.01\), as shown in Equation (1). The specific constitutive relationship curve of the steel material is shown in Figure 1.  
\[\varepsilon_{u}=\frac{f_{y}}{E_{S}}+\frac{\left(f_{u}-f_{y}\right)}{\alpha E_{ s}} \tag{1}\]  
This paper studies the plastic model of concrete damage based on ABAQUS software [20]. The model is suitable for monotonic and repetitive loading, with good convergence, making it particularly appropriate for simulating the behavior of concrete structures under low-frequency repetitive loads. Although ABAQUS provides various concrete constitutive models, it does not specify the stress-strain relationship of concrete, which needs to be defined independently. Therefore, given that the constitutive relationship of concrete has not yet been unified, this paper refers to the \"Code for Design of Concrete Structures\" (GB50010-2010) [21]. The single-axis compressive and tensile stress-strain relationship curves define the relevant equations (Figures 2 and 3). The following equations describe in detail the behavior of concrete under different stress states, including the stress-strain relationship under compression and tension, as well as the method used for calculating damage factors. Figure 1: Node detailing. Figure 2: Stress–strain curve of concrete under uniaxial compression. Under compression, the stress-strain relationship of concrete is given by Equations (2)-(5), which include key parameters such as the uniaxial compressive strength, peak tensile strain, and damage evolution parameters. Under tension, the stress-strain relationship is described by Equations (6)-(9), involving similar parameters. These equations and parameters together form the mechanical behavior model of concrete under different loading conditions. Additionally, this paper is based on the principle of Sidiroff energy equivalence [22]. The formula (10) for calculating the tensile and compressive damage factors of concrete was derived. These damage factors are crucial for simulating the damage evolution and stiffness recovery characteristics of concrete under repeated loads, and can more accurately reflect the actual behavior of concrete materials. The illustrative diagram is shown in Figure 4 below.