# Random Fiber Array Generation Considering Actual Noncircular Fibers with a Particle-Shape Library
## 4 Conclusions  
In this work, we generated RVEs considering actual noncircular fibers randomly selected from a particle-shape library, including the features of M55J. The RSE and RFR algorithms were employed to create RVEs various \(V_{f}\) along with proper modification to consider the noncircular fibers.  
To check the randomness of the proposed RVEs, we calculated spatial and physical metrics, concluded that the proposed method is sufficiently random, and reproduced experimental data in terms of the shapes and positions of actual fibers. In addition, to investigate the effect of the fiber shapes on the stiffness and strength of the composite, RVEs with circular fibers were also prepared. The material properties of M55J/M18 and T300/PR319 were adopted, and the effective elastic properties were compared. Based on the results, it is concluded that M55J/M18 having a low \(\mathbf{RR}_{T}\) showed minimal deviation according to the fiber shapes. However, in the case of T300/PR319, which has a high \(\mathbf{RR}_{T}\), the maximum deviation of \(G_{12}\) according to the fiber shapes was about 5%. Finally, to investigate the effect on the material fracture strength, the maximum von Mises stress in the matrix was compared with a tensile strain of 1% in the transverse direction according to the fiber shapes. The results showed that the maximum difference according to the fiber shapes of M55J/M18 was up to about 2%, but that of T300/PR319 was up to about 13%. Thus, from a practical point of view, when predicting the strength of composite using micromechanical models having a large \(\mathbf{RR}_{T}\) of the composites, it is necessary to consider the actual noncircular fiber shapes and positions in the micromechanics model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(V_{f}\) & **Methodology** & **Fiber Shape** & \multicolumn{2}{c}{**Maximum \(\sigma_{\
u}\) in Matrix (MPa)**} \\ \cline{3-5}  & & & **M55J/M18** & **T300/PR319** \\ \hline \multirow{4}{*}{60\%} & \multirow{4}{*}{RFR} & Circular (reference) & \multirow{2}{*}{46.065} & \multirow{2}{*}{73.756} \\  & & Noncircular (error in \%) & & (\(-1.66\%\)) & (\(8.83\%\)) \\ \cline{3-5}  & & Circular & 43.091 & 55.927 \\ \cline{3-5}  & & Noncircular & 43.461 & 61.341 \\ \cline{3-5}  & & Noncircular & (\(0.86\%\)) & (\(9.68\%\)) \\ \hline \multirow{4}{*}{55\%} & \multirow{4}{*}{RFR} & Circular & \multirow{2}{*}{45.104} & \multirow{2}{*}{75.978} \\  & & Noncircular & (\(-0.60\%\)) & (\(7.55\%\)) \\ \cline{3-5}  & & Circular & 41.757 & 43.953 \\ \cline{3-5}  & & Noncircular & (\(1.37\%\)) & (\(12.02\%\)) \\ \hline \multirow{4}{*}{45\%} & \multirow{4}{*}{RFR} & Circular & \multirow{2}{*}{43.605} & \multirow{2}{*}{59.081} \\  & & Noncircular & & (\(-1.19\%\)) & (\(11.28\%\)) \\ \cline{3-5}  & & Circular & 40.319 & 36.414 \\ \cline{3-5}  & & Noncircular & 40.863 & 41.036 \\ \cline{3-5}  & & Noncircular & (\(1.35\%\)) & (\(12.69\%\)) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the maximum von Mises stress in matrix.  
**Author Contributions:** Conceptualization, M.-S.G.; Funding acquisition, D.-S.H.; Supervision, J.H.L.; Writing--original draft, M.-S.G.; Writing--review and editing, M.-S.G., S.-M.P. and D.-W.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (No. 2020R1F1A1075588). Additionally, this research was supported by \"Research Base Construction Fund Support Program\" funded by Jeonbuk National University in 2019.  
**Conflicts of Interest:** The authors declare no conflict of interest.