## 4 Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Model** & **Contents** & **Unit** & **2\%** & **4\%** & **6\%** & **8\%** & **10\%** & **15\%** \\ \hline \multirow{3}{*}{ROM} & E11 & MPa & 1798.5 & 2272.0 & 2745.5 & 3219.0 & 3692.5 & 4876.3 \\ \cline{2-9}  & G11 & MPa & 632.0 & 831.7 & 1031.4 & 1231.1 & 1430.8 & 1930.0 \\ \cline{2-9}  & nu12 & - & 0.43 & 0.42 & 0.42 & 0.41 & 0.41 & 0.40 \\ \hline \multirow{3}{*}{Hobbs equation} & E11 & MPa & 1373.5 & 1423.9 & 1476.2 & 1530.4 & 1586.9 & 1738.2 \\ \cline{2-9}  & G11 & MPa & 448.5 & 465.3 & 482.8 & 501.0 & 519.9 & 570.8 \\ \cline{2-9}  & nu12 & - & 0.42 & 0.42 & 0.41 & 0.41 & 0.40 & 0.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical analysis result. observed as the volume fraction of UHMWPE increased. To determine this trend clearly, a comparative analysis was conducted using the graphs shown in Figure 3.  
The predicted modulus of elasticity of the PP-UHMWPE mixture is shown in Figure 3. Basically, because the modulus of elasticity of UHMWPE was approximately 19 times higher than that of PP, it can be considered that the higher the volume fraction of UHMWPE, the higher the modulus of elasticity of the mixture. For quantitative comparison of the difference between the predicted moduli of elasticity, the elastic index (EI) was calculated. The EI of the modulus of elasticity predicted using the ROM method was 236.8 MPa/vf%, that obtained using the Hobbs equation was 28.1 MPa/vf%, and that calculated by the finite element method (FEM) was 36.3 MPa/vf%. The shear modulus in Figure 4 is also expressed in terms of the shear index (SI) for quantitative comparison of the results. The SI of the shear modulus predicted using the ROM method was 99.8 MPa/vf%, that obtained from the Hobbs equation was 9.4 MPa/vf%, and that calculated by the FEM was 12.5 MPa/vf%. From these results, it can be judged that, in the prediction of the modulus of elasticity and shear modulus using the ROM model, the difference between the results obtained by FEM and the ROM model continued to increase with increasing volume fraction because the EI and SI were large. In general, the ROM model is linearly calculated according to the volume fraction of the reinforcing agent of the composite material, as shown in Equation (1); thus, as the volume fraction increased, the excellent physical properties of UHMWPE were linearly reflected, and the elastic properties increased. Additionally, since the elastic modulus of UHMWPE was 25,000 MPa, which is higher than the 1325 MPa of PP, the composite material was more elastic depending on the volume fraction. On the other hand, in the Hobbs equation, the physical properties are determined according to the volume fraction of the reinforcing agent, and the elastic modulus of the base material and the reinforcing agent is calculated by combining them. According to these estimation methods, there was a difference compared to the ROM model. As shown in Figure 5, because the Poisson's ratio of UHMWPE was smaller than that of PP, the Poisson's ratio decreased with the increasing volume fraction of UHMWPE. Figure 3: Comparison of modulus of elasticity. In this study, a composite reinforcing existing PP using UHMWPE particles was developed, and a numerical approach was employed to predict the elastic properties of the composite. Numerical calculations were performed using the ROM model and Hobbs equation, and the results of comparative analysis using FEA confirmed that the error was large in the case of the ROM model. Further, a trend in the values of the elastic properties similar to that of the FEM values was obtained using the Hobbs equation.