## 4 Finite Element Models  
ATENA, along with the GID pre-processor, was used to carry out the numerical analyses. Regarding the choice of materials, Cementitious2 material was used for concrete; a fracture-plastic model that considers the fracturing plastic behavior. Bilinear stress-strain curves were used to model the 15-mm-thick steel plates used for the loading plate, and pinned supports. The concrete beam, loading plate, and supports were all meshed with eight-node hexahedral elements, and stirrups and rebars were reinforced with 1-D truss elements embedded in concrete. The load was applied in a displacement-controlled manner with increments of 0.1 mm until failure occurred, considering the damage criterion [26]. Monitoring points were defined to obtain the reaction at the loading plate and deflection at the mid-span The Newton-Raphson method was used to solve the equations. Figure 3 shows a model (M8) of the reinforced concrete beam specimen, which was created using ATENA, to simulate the three-point flexure test. All the models were created supporting the details of each specimen. The results of the flexural stress and the maximum deflection of the specimens determined from the experimental tests were verified using the results of the numerical models obtained from ATENA. The verification process was necessary to verify the results of the experimental tests, and, as a result, the surrogate models would be a strong tool in predicting the responses of a structural system. Firstly, the flexural stress results of all specimens in the experimental tests were in excellent agreement with the results of the numerical models, see Figure 4 and Table 5. The maximum percentage error reached 2.79% for model M3, which is acceptable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Maximum Flexure** & \multirow{2}{*}{**Slope**} & **Flexural** & **Young’s Modulus** & **Maximum** & **Flexural Stress** \\  & **Load (kN)** & & **Strain(mm/mm)** & **(N/mm\({}^{2}\))** & **Deflection (mm)** & **(MPa)** \\ \hline \(1\) & 77.240 & 0.7140 & 0.1639 & 104.860 & 4.430 & 17.190 \\ \(2\) & 94.680 & 0.8330 & 0.1722 & 122.340 & 5.68 & 21.070 \\ \(3\) &  
Similarly, the results of the maximum deflection of all specimens in the experimental tests were in very good agreement with the results of the numerical models, as shown in Figure 5 and Table 6. The maximum percentage error reached 3.69% for model M3 again, which is acceptable. Figure 4: Flexural stress verification. Figure 3: Numerical model of the reinforced concrete beam (M8). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Flexural Stress ATENA** & **Flexural Stress** & \multirow{2}{*}{**Error \%**} \\  & **(MPa)** & **Experiment (MPa)** & \\ \hline
1 & 17.15611696 & 17.185900 & 0.17 \\
2 & 21.09721253 & 21.066300 & 0.15 \\
3 & 17.15664377 & 17.6468700 & 2.79 \\
4 & 21.59837950 & 21.591400 & 0.01 \\
5 & 17.95554714 & 17.635350 & 1.82 \\
6 & 21.44176454 & 21.782750 & 1.57 \\
7 & 20.31767836 & 20.447750 & 0.64 \\
8 & 20.70511776 & 20.817100 & 0.54 \\
9 & 17.09409603 & 17.521875 & 2.44 \\
10 & 16.3360424 & 16.74900 & 2.43 \\
11 & 21.15750459 & 21.667050 & 2.35 \\
12 & 24.50759912 & 23.963250 & 2.27 \\
13 & 20.92028772 & 20.899425 & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Error estimation for flexural stress. All the results were successfully verified with a satisfactory rate of error that did not exceed 5%. Only the maximum errors in both responses of flexural stress and maximum deflection occurred in specimen M3, which may have been due to many expected reasons: the asymmetric compaction of the specimen, error in applying the load, or improper contact between the load and the concrete surface. Moreover, we will consider two models, M4 and M9, to verify the results of the experimental tests by comparing both with the numerical simulations obtained from ATENA.