# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 3 Development of Finite Element Model for G40 Concrete and UHPFRC Using Non-Interface Element
### Mesh Discretisation  
In this simulation, concrete elements are conceptualised as a homogeneous material with support structures incorporating embedded elements, yet they feature a blind hole for the CFRP bar at both the top and bottom of the concrete. The modelling strategy adhered to a standardised, fine mesh with a global size of 20 mm, as depicted in Figure 3a. The specimens were discretised using eight-node, reduced-integration brick elements (C3D8R) for the concrete and two-node link elements (T3D2) for the steel reinforcement bars. Each C3D8R element has eight nodes with three degrees of freedom, making it suitable for 3D modelling of solids, with or without reinforcement. This element is adept at simulating concrete tension cracking, compression crushing, creep effects, and accommodating large  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Mass Density of Steel (Kg/m3)** & **Young’s Modulus (N/mm2)** & **Poisson Ratio** \\ \hline
8050 & 200,000 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Steel Reinforcement Properties.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Size (MPa)** & **Size (MPa)** & **Size (MPa)** \\ \hline
200 & 0 \\
246 & 0.0235 \\
294 & 0.0474 \\
374 & 0.0935 \\
437 & 0.1377 \\
480 & 0.18 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Plastic Criteria of Steel Stress–Strain Relationship.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**E11** & **E22** & **Nu12** = **Nu13** & **Nu23** & **G12** = **G13** & **G23** & **Density** \\
**(MPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(Tonne/mm3)** \\ \hline
130,000 & 8000 & 0.28 & 0.4 & 6 & 3.7 & \(1.56\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: CFRP Finite Element Properties.  
strain. Conversely, T3D2 elements are designated for one-dimensional reinforcement bars that primarily undergo axial deformation. The blind holes in the concrete were meticulously meshed using a seeding tool to achieve a finer mesh resolution. The partitioning of the model was employed to ensure a more precise mesh that promotes optimal bond strength and effective load transfer within the system. The CFRP rod was also subjected to meshing as a three-dimensional element with a 15 mm mesh size, as illustrated in Figure 3b.  
Furthermore, a mesh sensitivity analysis was executed to determine the effect of mesh size on the outcomes. Although finer meshing is typically anticipated to produce more accurate results, the analysis revealed that mesh sizes ranging from 5 mm to 20 mm provided similar results. Thus, to curtail computational processing time and minimize roundoff errors, a mesh size of 20 mm was selected as standard. It is important to emphasize that the ideal mesh size is inherently dependent on the specifics of the model, indicating that different models may necessitate different optimal mesh sizes. With this refined understanding of the mesh size, sensitivity analysis has been duly integrated into the discussion to clarify the methodological choices made during the modelling process.