## 2 Materials and Methods  
The FEA prediction of fiber structure is largely dependent on the textile 3D models. Conditions such as the twisted structure of the fiber, the material model, and the associated contact boundary conditions should all be considered. Furthermore, modeling is complicated by the nonuniform structure of the 3D textiles and the spatially variable material properties caused by the fiber architectures. Realistic textile geometries should be considered to effectively predict the performance of 3D woven textiles and composites. There are two types of finite element textile models that represent textile microstructures, namely the macroscale continuum and discrete approaches. Furthermore, textiles can be modeled as homogeneous materials at the macroscopic level [32; 33; 34]. A discrete mesoscopic analysis can be performed based on the yarn structure. The microscale approach can be used to model the representative methods of fibers in the yarn structures in textiles [35; 36; 37]. Micro- and meso-scopic simulations enable deformation analysis during the preforming process and fiber structure construction during the resin injection step. Thus, in this study, an FEA model was generated using micro-modeling to analyze the elastic properties of composites. Figure 1 shows the basic 3D model and tensor notation used in this study. Tensors are illustrated according to the direction of stress to analyze the composites composed of UHMWPE textiles. Here, E represents the elastic modulus, while 1, 2, and 3 represent the x, y, and z axes, respectively. Furthermore, G represents the shear stress applied to the composite surface, and the tensor is expressed by the subscript m for the PP matrix and w for textiles. The properties of PP and UHMWPE used in this study are listed in Table 1[12; 38]. The measured physical properties were based on commercial products. The physical properties of PP were based on Adstif EA5074, manufactured by Polymirae Co., Ltd., (Seoul, South Korea) while those of UHMWPE were based on MILLON XM-220, manufactured by Mitsui Chemical. The materials used were characterized as linear isotropic materials according to their qualities. However, these isotropic materials may be used as anisotropic materials based on the geometry of UHMWPE in the textiles modeled using the ANSYS Material  
Figure 1: Three-dimensional model and tensor notations. Designer software. Consequently, depending on the modeled structure, the physical properties may appear as anisotropic material properties in FEA analysis. FEA was used for 3D modeling of composites with UHMWPE textiles using the ANSYS Material Designer software and a homogenization approach. Homogenization theory was used to compute the effective properties of materials or composites with periodic structures. The simulations were performed based on the assumption that the structure is composed of a continuous network of infinitely small unit cells [39; 40; 41]. In the case of FEA using homogenization theory, the boundary conditions are symmetrical in all planes. Figure 2 shows the implementation of the 3D model of the composite material based on homogenization theory. A virtual RVE was constructed, and the volume was set to Matrix PP for 3D modeling of PP composites with UHMWPE textiles. The UHMWPE fibers were placed within the PP RVE. Subsequently, 3D modeling was conducted by determining the volume occupied by the UHMWPE textiles in the total composite and by adjusting the volume fraction from 45% to 75% in 5% increments. The fundamental modeling criteria were determined based on the volume fraction such that the oriented UHMWPE textiles were organized in the PP matrix. The element type used for FEA was SOLID187, with a mesh size of 0.5 \(\upmu\)m. Because SOLID187 supports the implementation of secondary displacement, it is ideal for creating meshes inside irregularly shaped structures. To reduce the sensitivity of predicting physical properties based on mesh size, the elements used for the PP matrix and UHMWPE fiber were set to the same size.