# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 7 Development of Interface Element
Degradation commences when the stresses and strains meet specific damage initiation criteria that have been predetermined. Various damage initiation criteria exist, and each damage initiation criterion also has an output variable associated with it to indicate whether the criterion has been met. A value of 1 or higher signifies that the initiation criterion has been fulfilled. In this article, the maximum nominal stress criterion is employed. Damage is assumed to initiate when the maximum nominal stress ratio reaches a value of 1. \[\text{max}\left\{\frac{\langle t_{n}\rangle}{t_{n}^{a}},\frac{\langle t_{s} \rangle}{t_{s}^{a}},\frac{\langle t_{t}\rangle}{t_{t}^{a}}\right\}=1 \tag{24}\]  
Furthermore, a general contact has been defined as surface-to-surface with minor slip criteria between the CFRP and concrete interface. A \"tangential behaviour\" with a penalty of 0.3 has been established. Additionally, to preclude any penetration, the normal behaviour has been designated as a rigid \"contact\". Another interaction has been defined between the CFRP and concrete interface based on the analytical results formulated in this research. The contact property is specified as \"cohesive behaviour\", which is a thin layer serving as an interface that determines the bonding strength of the CFRP-concrete element. The cohesive behaviour data are presented in Table 13.  
Additionally, damage initiation parameters with a quadratic traction criterion have been utilised, as shown in Figure 22. The corresponding data are presented in Table 14.  
Furthermore, the damage evolution was also considered as linear displacement with a total displacement of 1 mm. This implies that if the bonding at the CFRP-concrete interface exceeds 1 mm, the test is deemed to fail at that point. Additionally, the viscosity is also 1 mm. The normal behaviour was assigned as a rigid \"contact\", and the tangential behaviour at the CFRP-concrete interface was considered with a friction coefficient of 0.75. The shear stress was specified as 3.9 MPa and the elastic slip was considered as 0.00001. Notwithstanding the general contact that was previously defined, the surfaces of the CFRP that are embedded in concrete will adhere to the cohesive behaviour and are considered exceptions to the general contact to have their own behaviour. Ultimately, the simulation was conducted on two 2D six-node specimens, one with the interface element that was analytically obtained \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{K_{nn}}\) (MPa) & \(\mathbf{K_{ss}}\) (MPa) & \(\mathbf{K_{tt}}\) (MPa) \\ \hline
1.5 & 360 & 360 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Cohesive Behaviour Interaction. and the other without an interface element. The maximum stress in Figure 23a indicates that the CFRP rod performs optimally with UHPFRC, with the bonding holding up until the CFRP material itself fails. On the other hand, the displacement results also show that the maximum displacement occurred in the CFRP material while the UHPFRC was also deformed (Figure 23b). The damage propagation in G40 concrete is shown in Figure 24a. The interface at the CFRP has been compromised by 80%, including the tip of the CFRP rod at the inside of the embedded region. The minimal bonding area is caused by angular and coarse aggregate that interlocks with the CFRP, but it is not satisfactory because the debonding exceeds 1 mm. On the other hand, the damage propagation in UHPFRC reveals robust bonding with minimal damage compared to G40 concrete. Notably, no debonding is apparent, attributed to the ductility and interlocking performance of UHPFRC with CFRP rods (Figure 24b). The force-displacement curve depicted in Figure 25 illustrates data acquired from the sample with an interface element subjected to cyclic loading for G40 concrete. The maximum force recorded reached 75 kN at a displacement of 12.9 mm.