## 3 Modeling of the Steel-Concrete Composite Beam  
### The Solid-Slipping Beam Model  
To simulate the spatial stress and nonlinearity of SCCB, the Traditional Beam Model (TBM) method has been widely utilized [18]; however, the TBM assumes that the concrete slab and steel beam work together and simulates shear connectors by setting the stiffness function of spring elements or truss elements, which cannot reflect the slight changes in shear connectors and the surrounding concrete. In recent years, the solid-slipping beam model (SSBM) was favored by researchers due to its superiority in escaping the dependence on the stiffness-slip function [19]. To construct the SSBM for steel-concrete beams, the formulation of the model geometry, element types, material behavior, and solution technique is challenging; detailed descriptions are outlined as follows:  
**(1) Element types and meshes**  
To simulate the local stress effects of shear studs and surrounding concrete, the 8-node linear brick element (C3D8R) was proposed for concrete slab, steel beam, and headed shear studs. The 8-node linear brick is a reduced-integration solid continuum element with a Gauss integration point and is less prone to shear self-locking under bending load. Moreover, the hexahedral element has a better convergence rate than other solid elements, and the calculation accuracy is not significantly affected by sensitivity to mesh orientation. The T3D2 truss element with two nodes and three translational degrees of freedom was proposed for steel bars. The steel truss was embedded into the concrete slab, and no moments or forces perpendicular to the centerline were supposed. The T3D2 (truss) and C3D8R (brick) elements were connected by tie constraints, where the relative slip between steel bars and surrounding concrete was ignored. All entities were sliced according to the principles of symmetry and deformation compatibility. To ensure good meshing quality and reduce the hourglassing effect, the structured grid technology and advancing front algorithm were adopted, and the hourglass control option in ABAQUS was enabled. Additionally, a refined grid for the headed shear studs and surrounding concrete was conducted, which will be detailed in Section 3.2, Section 3.3, and Section 4.1. **(2) Material modeling**  
Concrete has significant anisotropy and stress complexity. The concrete damaged plasticity (CDP) model has been proven to be a granted choice because the CDP model can reflect the mechanical properties of concrete under both tensile and compressive stress and handle local stress concentration effectively [20,21]. In this study, the CDP model was adopted for concrete when conducting the mechanical performance analysis in the corresponding sub-section. In the CDP model, the nonlinear (elastic-plastic) mechanical behavior of the concrete was presented by an equivalent uniaxial stress-strain curve based on Euro Code 2 (EC2) [22], as shown in Figure 3a. For concrete in compression, three parts of the curve can be identified. The first part was initially assumed to be linear elastic up to \(0.4f_{\text{ck}}\), where \(f_{\text{ck}}\) is the compressive cylinder strength of the concrete. The initial modulus of elasticity of the concrete was recommended by EC2, as in Equation (10). [PERSON]'s ratio of concrete is taken as 0.2. \[E_{\text{cm}}=0.95\times(f_{\text{ck}}+8)^{1/3}\ (E_{\text{cm}}\ \text{in}\ \text{GPa},f_{\text{ck}}\ \text{in}\ \text{MPa}) \tag{10}\]The second part of the curve was the non-linear parabolic portion starting from the proportional limit stress \(0.4f_{\rm ck}\) to the peak stress \(f_{\rm ck}\), which can be determined from Equation (11):  
\[\sigma_{\rm c}\ =\ \bigg{(}\frac{kn-n^{2}}{1+(k-2)n}\bigg{)}f_{\rm ck} \tag{11}\]  
where \(n=\varepsilon_{\rm c}/\varepsilon_{\rm cl}\), \(\varepsilon_{\rm cl}\) represents the strain at peak stress (\(\varepsilon_{\rm cl}\) = 0.0022), and \(k=1.1E_{\rm cm}\times\varepsilon_{\rm cl}/f_{\rm ck}\); \(f_{\rm ck}\) represents the compressive cube strength of the concrete.