## 3 Results and Discussion  
### Model Validation  
The validation of the numerical model has been conducted by comparing the force-deflection diagrams obtained experimentally [16] and numerically for all of the analyzed models (Figure 13a-e). Based on a comparative analysis of the numerical and experimental load-deflection ratios, one may notice very good agreement of the results up to failure, which confirmed the model validation. Full agreement of the results has been achieved in the first and second load-deflection branches for all of the analyzed models, i.e., in the elastic regime and after the crack opening up to the steel reinforcement yield. A slight disagreement of the results is noticeable in the third branch of the load-deflection diagrams. Namely, after the yield of the steel reinforcement, a sudden loss in beam stiffness occurs. Due to the highly nonlinear problem, at this stage some discrepancy in the numerical and experimental results occurs. Nonlinear phenomena in this problem are caused by concrete cracking, steel reinforcement yielding, concrete crushing in the compression zone, the bonding effect between the concrete and the epoxy, and the heterogeneity of the concrete in the experimental beams. Considering all of the abovementioned conditions, one may conclude that the obtained numerical results are in good agreement with the experimental ones. Certain deviations have been noticed for the beams B-G2 and B-G4. Model B-G2 is with the cut-off of the strengthening FRP bar in the midspan, but without bypassing (splicing). Therefore, after the steel reinforcement yield, an abrupt development of a crack in the midspan occurs, leading to the loss of the effectiveness of the additional FRP bar and causing the beam behavior to be similar to that of the control beam without FRP strengthening. This highly nonlinear effect influenced the slight disagreement in the numerical and experimental results (Figure 13c). On the other hand, model B-G4 showed somewhat higher stiffness (Figure 13e) because of the longer groove filled with epoxy, which possesses better mechanical characteristics than those of concrete. After the moment of the steel reinforcement yield and sudden crack propagation, the numerical results are stabilized, indicating a convergence towards the experimental results. Considering everything mentioned, the numerical models can be treated as reliable in the sense of the load-deflection ratios of the analyzed models. The failure mechanism represented by crack propagation, as well as the shear stress propagation (bond stress) at the contact of the epoxy and the concrete, has also been analyzed. Exceeding this stress proved to be the main cause of failure. A comparative analysis between the numerical and the experimental test has been conducted, considering both parameters (the cracks and the bond effect). It has to be mentioned that the crack development in the CDP model has been defined via the damage parameter in tension. Other research recommends that a crack opens at strains several dozen times greater than the strain at tension strength [45; 46]. In this research, the value of the damage parameter, d\({}_{\rm t}\), of 0.80, which corresponds to a strain 50 times greater than the strain at tension strength, has been adopted as the crack opening. Representative models for the analysis of the cracks and bond stresses were B-G1, without the cut-off of GFRP reinforcement, and B-G4, with cut-off bypassing realized via supplemental GFRP bars of 40\(\O\) (40 cm) in length. One may conclude that cracks open uniformly at the strengthened beam without GFRP cut-off, and that cracks do not intersect the epoxy because it has a higher tensile strength (Figure 14). On the concrete-epoxy interface, a maximal contact shear stress of 3 MPa has been reached. As a consequence, slippage of the epoxy occurs, which leads to the relocation of the critical zone and to the redistribution of the shear stresses. This is more prominent in the region starting from the load application zone towards the supports (Figure 15).