# Random Fiber Array Generation Considering Actual Noncircular Fibers with a Particle-Shape Library
## 3 Results and Discussion
### Comparison of the Results between Actual Noncircular Fibers and Circular Fibers
#### 3.2.1 Comparison of the Effective Elastic Properties
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Elastic Properties** & **M55J** & **M18** & **Relative Ratio** & **T300** & **PR319** & **Relative Ratio** \\ \hline \(E_{1}\) (GPa) & 496.52 & 3.5 & 141.8629 & 230 & 0.95 & 242.1053 \\ \(v_{12}\) & 0.25 & 0.38 & 0.6579 & 0.2 & 0.35 & 0.5714 \\ \(E_{2}\) (GPa) & 6.38 & 3.5 & 1.8229 & 15 & 0.95 & 15.7895 \\ \(G_{23}\) (GPa) & 2.78 & 1.2681 & 2.1923 & 7.0093 & 0.3519 & 19.9184 \\ \(G_{12}\) (GPa) & 17.92 & 1.2681 & 14.1314 & 15 & 0.3519 & 42.6258 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Elastic properties of fibers and matrices and the relative ratio. 10a. This is because the deviation in \(V_{f}\) of RVE with noncircular fiber is larger than that of RVE with circular fiber as discussed in Section 3.2. Figure 8: Effective elastic properties: (**a**) \(E_{1}\), (**b**) \(E_{2}\), (**c**) \(G_{23}\), and (**d**) \(G_{12}\) of T300/PR319, with \(V_{f}\) ranging from 5% to 60%. Figure 7: Effective elastic properties: (**a**) \(E_{1}\), (**b**) \(E_{2}\), (**c**) \(G_{23}\), and (**d**) \(G_{12}\) of M55J/M18, with \(V_{f}\) ranging from 5% to 60%. Figure 10: Effective elastic properties: (**a**) \(E_{1}\), (**b**) \(E_{2}\), (**c**) \(G_{23}\), and (**d**) \(G_{12}\) of T300/PR319, with \(V_{f}=60\%\). Figure 9: Effective elastic properties: (**a**) \(E_{1}\), (**b**) \(E_{2}\), (**c**) \(G_{23}\), and (**d**) \(G_{12}\) of M55J/M18, with \(V_{f}=60\%\). Additionally, it should be noted that, in the case of M55J/M18, the deviations of the transverse moduli \(E_{2}\), \(G_{23}\) are minimal regardless of the fiber shape and the algorithm of random RVEs. However, the other transverse modulus \(G_{12}\) varies according to the fiber shape and the algorithm of random RVEs. In the case of T300/PR319, all transverse modulus \(E_{2}\), \(G_{23}\), and \(G_{12}\) show large deviations according to the RFR and RSE algorithms, and as \(V_{f}\) increases, the deviation increases. For example, for \(V_{f}=60\%\) with the RFR algorithm, the deviation of \(G_{12}\) according to fiber shape is 4.33%, which is larger than that of M55J/M18 (=2.58%). As mentioned earlier, it could be because \(\mathbf{RR}_{\mathrm{T}}\) of the M55J/M18 composite is not significant compared to that of T300/PR319. Although the difference in the effective elastic properties according to the fiber shape of M55J/M18 is small, the actual noncircular fiber shapes should \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(V_{f}\) & **Algorithm** & **Fiber Shape** & \(E_{1}\)**(GPa)** & \(E_{2}\)**(GPa)** & \(G_{23}\)**(GPa)** & \(G_{12}\)**(GPa)** \\ \hline \multirow{4}{*}{60\%} & RFR & Circular (reference) & 300.455 & 5.431 & 1.995 & 4.735 \\  & & Noncircular (error in \%) & 299.028 & 5.420 & 1.989 & 4.857 \\  & & Circular (error in \%) & (\(-\)0.47\%) & (\(-\)0.20\%) & (\(-\)0.30\%) & (2.58\%) \\  & RSE & Circular & 300.425 & 5.429 & 1.996 & 4.492 \\  & & Noncircular (\(-\)0.45\%) & (\(-\)0.11\%) & (\(-\)0.25\%) & (0.65\%) \\ \hline \multirow{4}{*}{55\%} & RFR & Circular & 274.915 & 5.306 & 1.914 & 4.209 \\  & & Noncircular & 274.670 & 5.302 & 1.912 & 4.326 \\  & & (\(-\)0.09\%) & (\(-\)0.08\%) & (\(-\)0.10\%) & (2.78\%) \\  & RSE & Circular & 274.881 & 5.304 & 1.915 & 3.800 \\  & & Noncircular & 274.238 & 5.301 & 1.913 & 3.844 \\  & & (\(-\)0.23\%) & (\(-\)0.06\%) & (\(-\)0.10\%) & (1.16\%) \\ \hline \multirow{4}{*}{45\%} & RFR & Circular & 223.827 & 5.060 & 1.764 & 3.282 \\  & & Noncircular & 225.372 & 5.065 & 1.768 & 3.388 \\  & & (\(0.69\%\)) & (\(0.10\%\)) & (0.23\%) & (3.23\%) \\ \cline{1-1}  & RSE & Circular & 223.801 & 5.057 & 1.765 & 3.001 \\ \cline{1-1}  & & Noncircular & 225.299 & 5.065 & 1.769 & 3.056 \\ \cline{1-1}  & & (\(0.66\%\)) & (\(0.16\%\)) & (0.23\%) & (1.83\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the effective elastic properties of M55J/M18.