## 4 Results
As the trend of the simulations aligned with the experimental results, the next stage in the research was to refine the determination of the optimal FWR content. With this aim, intermediate values between FWR = 20 kg/m\({}^{3}\) and FWR = 40 kg/m\({}^{3}\) were simulated, as no experimental data were available for these ranges. The simulation results are presented in Figure 4.  
Interestingly, the simulations reveal a trend that was not achieved in the experiments. It can be noticed that energy dissipation is enhanced with an increasing fiber content up to 27.5 kg/m\({}^{3}\) FWR and at the optimum value at this content. Energy dissipation drops above 27.5 kg/m\({}^{3}\) FWR, which indicates that a fiber content that is too high decreases ductility and strain capacity. As seen in Figure 5, this result revealed through simulations over a denser range of FWR values from 20 to 40 kg/m\({}^{3}\) demonstrates the benefit of refining the optimization of fiber content with computational modeling. At the next stage, it was examined how different compressive strengths affect the optimal fiber content. With this aim, the same fiber contents were used in different types of concrete with a compressive strength of 120 MPa. The simulated stress-strain curves obtained for concrete with a compressive strength of 120 MPa and FWR = 0, 20, 30, 40, and 60 kg/m\({}^{3}\) are shown in Figure 6. To extend the model for 120 MPa concrete, the LDPM parameters were recalibrated accordingly. The compressive yielding strength parameter (confined) \(\sigma_{\rm{C0}}\) was adjusted to 240 MPa, while the shear-to-tensile ratio parameters were modified to \(\sigma_{\rm{s}}/\sigma_{\rm{t}}\) = 4.54. Figure 5: Load–strain response for various FWRs ranging from 20 to 40 kg/m\({}^{3}\). The overall trend is consistent with the 90 MPa concrete results, where an FWR of 30 kg/m\({}^{3}\) provides the best energy dissipation performance. Table 5 presents the changes to examine the effect of compressive strength on energy dissipation. The compressive strength effect is seen in the slope and extent of energy dissipation change. The first fiber reinforcement from 0 to FWR = 20 kg/m\({}^{3}\) results in a sharp relative increase (\(\sim\)339%) in the lower-strength 90 MPa concrete compared to the 120 MPa concrete (\(\sim\)188%), indicating that fibers have a greater influence on enhancing the ductility of the weaker concrete. However, while this growth occurs rapidly, the absolute magnitude of energy dissipation is higher for 120 MPa concrete at any FWR level. Specifically, the FWR = 27.5 kg/m\({}^{3}\) is the peak point of energy dissipation for both concretes under simulation, wherein the highest peak dissipation rate is achieved at 5.87 for the 120 MPa concrete and at 1.82 for the 90 MPa concrete, demonstrating a remarkable improvement in comparison to the lower and higher contents of fibers. This comparison is an important discovery, as earlier experimental results revealed that FWR = 30 kg/m\({}^{3}\) was the best  
Figure 6: Stress–strain curves obtained for concrete with a compressive strength of 120 MPa at different FWR values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**FWR** & \multicolumn{2}{c}{**120 MPa**} & \multicolumn{2}{c}{**90 MPa**} \\ \cline{2-5}
**[kg/m\({}^{3}\)]** & **Simulation** & **Change (\%)** & **Simulation** & **Change (\%)** \\ \hline
0 & 0.926 & & 0.189681 & \\
20 & 2.67 & 188.34 & 0.8328 & 339.05 \\
27.5 & 5.87 & 119.85 & 1.82 & 118.54 \\
30 & 5.71 & \(-\)2.73 & 1.71 & \(-\)6.04 \\
40 & 4.712 & \(-\)17.48 & 1.43918 & \(-\)15.84 \\
60 & 3.676 & \(-\)21.99 & 0.819698 & \(-\)43.04 \\ \hline \hline \end{tabular}  
* The “Simulation” columns represent the total energy dissipated calculated from the simulation, while the “Change (“c)” columns indicate the percentage change in energy dissipation between fiber contents.  
\end{table} 
Table 5: Comparison of energy dissipation between concrete with compressive strengths of 90 MPa and 120 MPa at different FWR values. fit.