## 2 Finite Element Modeling and Validation
### Establishment of the Finite Element Model
#### 2.2.2 Bond-Slip Model at the Strengthening Layer-Concrete Interface  
The FRP grid and the RC beam achieve bonding and force transfer through the use of polymer cement mortar. Therefore, in the finite element modeling of this section, the FRP grid is embedded in the PCM to form an integral strengthening layer, and the interaction relationship between the two is reflected by adding a bonding layer between the concrete and the strengthening layer. Existing research [19; 20] shows that the bilinear bond slip constitutive model has relatively high accuracy in simulating the mechanical response between the strengthening layer and the concrete. Among them, the calculation method of the interfacial bond slip constitutive model proposed by [PERSON] et al. [21] is simple and has a wide application range, and it has been widely used by domestic and foreign researchers. The calculation formulas are shown in Equations (10)-(14), and the relationship curve is shown in Figure 4. In order to represent the above-mentioned bonding layer in ABAQUS, a Cohesive Element component with a thickness of 1 mm is established and placed between the strengthening layer and the concrete, and is tied to both of them using the Tie constraints. To characterize the performance of this bonding layer, it is necessary to determine key parameters such as the interfacial shear stiffness \(K_{0}\), the maximum interfacial shear stress \(\tau_{max}\), the interfacial ultimate slip \(s_{f}\), or the interfacial fracture energy \(G_{f}\). They obtained these parameters by substituting the relevant parameters of the test beam into the formula. The interface shear stiffness \(K_{0}\) is the ratio of \(\tau_{max}\) to \(s_{0}\), \(K_{0}=76.9\) GPa/mm.  
In the post-processing of ABAQUS, the debonding of the interface is judged by the SDEG (Scalar Stiffness Degradation) in the output file. The value of SDEG generally ranges  
Figure 4: Constitutive relation of bond slip behavior at the interface.  
Figure 3: Stress–strain relation curve of steel bar and the FRP grid.  
from 0 to 1. The closer the value is to 1, the more severe the damage degree is. When SDEG is 1, it indicates that debonding has occurred:  
\[\tau=\left\{\begin{array}{ll}\tau_{max}s/s_{0}&(0<s\leq s_{0})\\ \tau_{max}(s_{f}-s)/(s_{f}-s_{0})&(s_{0}<s\leq s_{f})\end{array}\right. \tag{10}\]  
\[\tau_{max}=\alpha_{1}\beta_{\omega}f_{t} \tag{11}\]  
\[s_{0}=0.0195\beta_{\omega}f_{t} \tag{12}\]  
\[s_{f}=2G_{f}/\tau_{max} \tag{13}\]  
\[G_{f}=0.308\beta_{\omega}^{2}\sqrt{f_{t}} \tag{14}\]  
\[\beta_{\omega}=\sqrt{\frac{2-b_{f}/b_{c}}{1+b_{f}/b_{c}}} \tag{15}\]  
where \(\tau\) and s are the local interfacial shear stress and relative slip; \(\tau_{max}\) and \(s_{0}\) are the local interfacial shear stress and relative slip; \(s_{f}\) is the corresponding slip when the interfacial shear stress is 0; \(G_{f}\) is the interfacial fracture energy; \(f_{t}\) is the tensile strength of concrete; \(\alpha_{1}\) is the finite element method to calculate the regression parameters, and its value is taken as 1.5; \(\beta_{\omega}\) is taken as the width influence coefficient; and \(b_{f}\) and \(b_{c}\) are the width of the FRP grid and the concrete section, respectively.