## 4 Results  
The experimental results were further simulated for the tests of fiber-reinforced concrete cylinder specimens with fiber weight ratio (FWR) values of 0, 20, 30, 40, and 60 kg/m\({}^{3}\)[10], highlighting the effect of fiber content on structural performance. Following the available experimental data, three cylindrical specimens (30 cm high and with a diameter of 15 cm) were tested for each fiber content. The presence of the fibers led to significant enhancements in the ultimate displacements obtained in the experiment, and their main contributions were toward plastic energy dissipation (PED). Numerical simulations in the frame of this present study have been performed in order to simulate the experimental results on the displacement behavior, energy dissipation, and ductility enhancement noted for the tested specimens. A detailed comparison between the experimental and simulated results for load strain for FWR of 0, 20, 30, 40, and 60 kg/m\({}^{3}\) is presented in Figure 3.  
Figure 3: Load–strain curves for varying FWRs. First, the experimental and calculated values of dissipated energy from the hysteresis loop were compared. The dissipated energy, \(W\), can be expressed as:  
\[W=\int_{unloading}Load\cdot de \tag{12}\]  
For FWR = 0 kg/m\({}^{3}\), the experimental measurements indicate zero energy dissipation (see Table 4), whereas the simulations yield a non-zero value of 0.189681 kN/m. This discrepancy is most likely due to measurement limitations rather than an issue with the numerical model. In brittle materials like plain high-strength concrete, failure occurs rapidly after reaching the peak load, making it challenging to capture post-peak energy dissipation experimentally. Since no data were recorded after the peak load in the experiments, the dissipation reported is considered zero, although in reality, some energy dissipation occurs. The simulation, however, captures the post-peak response computationally, accounting for residual dissipation that remains unmeasured in the experimental setup. Since one of the factors affecting the energy dissipation is the crack opening effect, it was examined for different fiber contents. Figure 4 shows the results for the investigated fiber contents. The extracted crack data reveal that the fiber content significantly influences cracking behavior and energy dissipation. As FWR increased from 20 to 30 kg/m\({}^{3}\), the number of cracks decreased by 6.15%, correlating with the highest observed energy dissipation at 30 kg/m\({}^{3}\) due to effective crack bridging and distributed micro-cracking. This indicates that fibers at this level enhance ductility and resistance to crack propagation, maximizing \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**FWR**} & **Experiment** & **Simulation** & \multirow{2}{*}{**Error [\%]**} \\  & **[kNm/m]** & **[kNm/m]** & \\ \hline
0 & 0 & 0.189681 & \\
20 & 1.075 & 0.8328 & 22 \\
30 & 1.887 & 1.71 & 9.38 \\
40 & 1.632 & 1.43918 & 11.81 \\
60 & 0.31 & 0.819698 & 62.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the dissipated energy obtained in the experiment results and the simulation results. Figure 4: Total crack opening values and patterns: (**a**) FWR = 20 kg/m\({}^{3}\), (**b**) FWR = 30 kg/m\({}^{3}\), (c) FWR = 40 kg/m\({}^{3}\), (d) FWR = 60 kg/m\({}^{3}\). energy dissipation. However, beyond 30 kg/m\({}^{3}\), the number of cracks increased--by 4.81% at 40 kg/m\({}^{3}\) and 9.51% at 60 kg/m\({}^{3}\)--suggesting that excessive fiber content leads to matrix saturation, fiber clumping, and localized stress concentrations. These factors reduce ductility and shift the failure mode from fiber pull-out to fiber breakage, diminishing energy dissipation. Thus, while moderate fiber content (30 kg/m\({}^{3}\)) optimizes energy absorption, higher fiber volumes compromise performance due to increased crack formation and reduced strain capacity.