## 3 Homogenization Method  
Homogenization techniques have received increasing attention for predicting the mechanical properties of composite materials over the past decades [26; 27; 28], because homogenization techniques can efficiently quantify the interplay between microscopic and macroscopic properties [29, 30, 31]. In this study, to predict the effective values of the elastic properties of composite materials, representative volume elements (RVE) were composed according to the UHMWPE volume fraction using specialized software (Ansys Material Designer), and the changes in the effective elastic properties of the material according to the UHMWPE volume fraction were comparatively analyzed using a numerical approach.  
To develop a numerical model required for the homogenization method, UHMWPE was applied as the particle-reinforced material, and a spherical shape with a diameter of 10 \(\upmu\)m was used for modeling. The material for the matrix was PP, considering the size of the particle-reinforced material. As shown in Figure 1, the matrix was modeled as a cube with dimensions of 40 \(\upmu\)m \(\times\) 40 \(\upmu\)m \(\times\) 40 \(\upmu\)m. In addition, to reflect the fact that UHMWPE was present as particles inside the cube-shaped matrix, an RVE model with an irregular arrangement of the particles was developed. The use of homogenized material data significantly lowers the computational cost of composite simulations, as the structure only needs to be simulated on a macroscopic scale.  
The mesh size of the RVE model with an increased volume of UHMWPE-particle-reinforced material was increased to 2 \(\upmu\)m, and the numerical models with different volume fractions are presented in Figure 2. The models consisted of the arrangement of randomly formed UHMWPE according to the volume fraction. The modeling algorithm of the random deployment of UHMWPE was as follows. To minimize variability in physical properties in composites due to excessive random arrangement, it was set that the powder of UHMWPE was added based on the existing 2% (VF). Therefore, although the random arrangement of UHMWPE was constructed, it was expected that interpretation with a certain tendency would be performed. The node and element information are summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Unit** & **2\%** & **4\%** & **6\%** & **8\%** & **10\%** & **15\%** \\ \hline Node & Ea & 113,767 & 113,211 & 118,315 & 119,491 & 121,788 & 127,324 \\ \hline Element & Ea & 79,752 & 79,468 & 82,908 & 83,584 & 85,213 & 88,649 \\ \hline \end{tabular}
\end{table}
Table 1: Number of elements in finite element analysis.  
Figure 1: UHMWPE-particle-reinforced PP composite employed for RVE modeling.  
In addition, the mechanical properties of the PP and UHMWPE used for this analysis are summarized in Table 2. The numerical approach and FEA method enabled prediction of the elastic properties of the mixture according to the volume fraction based on the basic properties of PP and UHMWPE presented below.  
Because the difference between the moduli of elasticity of the PP and UHMWPE used in this study was large, it can be judged that the higher the volume fraction of UHMWPE, the higher the modulus of elasticity of the mixture. In addition, considering that the Poisson's ratio of UHMWPE was 0.2 and that of PP was 0.43, it was expected that the Poisson's ratio of the mixture would be lower than 0.43.