## 2 Materials and Methods  
Figure 1 shows the tensor notation used in this study. The fibers were evenly oriented in the matrix; they form a composite material. The elastic modulus in the longitudinal direction of the matrix is denoted by E. The x-, y-, and z-axes are numbered 1, 2 and 3, respectively. The shear modulus on each side of the composite material is denoted by G. According to this tensor notation, G\({}_{12}\) implies that the shear stress occurs in the y-axis direction from the x-axis plane. This tensor notation can be applied equally to the fiber. The aspect ratio is defined as the length-to-diameter ratio of the fiber. In addition, considering the redundancy of the tensor representation, the superscript'm' is used for the tensor notation of the PP matrix, and the superscript 'f' is used for the tensor notation of the UHMWPE fiber. Various micromechanical models have been developed to numerically predict the elastic behavior of composite materials. Micromechanics is an analytical technique used to determine the number of individual components that make up a composite or heterogeneous material. Representatively, various analysis techniques exist, such as the rule of mixture (ROM), Chamis model, and Mori-Tanaka model. Among them, the Halpin-Tsai model has a reinforcing factor that can represent the aspect ratio; therefore, it can predict the behavior of the composite material according to the aspect ratio of the fiber. [PERSON] and [PERSON] (1969) developed a semi-empirical method for predicting composite properties. The method sensibly interpolates between the upper and lower bounds of composite properties. The Halpin-Tsai model is a mathematical model that predicts the elasticity of composites based on the shape and direction of the filler and the elastic properties of the filler and matrix [31; 32; 33; 34]. In addition, as shown in Equations (1)-(9), this model uses the experimentally-derived reinforcing factor (\(\xi\)) and correction coefficient (\(\eta\)) to improve the existing ROM. The reinforcement factor depends on the shape of the fibers, their arrangement, and load conditions. \[E_{11}=E_{m}\frac{\left(1+\xi_{11}\eta_{11}V_{f}\right)}{\left(1-\eta_{11}V_{ f}\right)} \tag{1}\]  
Figure 1: Tensor notation of fiber-reinforced composite materials. \[E_{22}=E_{m}\frac{\left(1+\xi_{22}\eta_{22}V_{f}\right)}{\left(1-\eta_{22}V_{f} \right)} \tag{2}\]  
\[G_{12}=G_{m}\frac{\left(1+\xi_{12}\eta_{12}V_{f}\right)}{\left(1-\eta_{12}V_{f} \right)} \tag{3}\]  
\[\xi_{11}=2(l\times t)+40(V_{f})^{10} \tag{4}\]  
\[\xi_{22}=2(w\times t)+40(V_{f})^{10} \tag{5}\]  
\[\xi_{11}=(w\times t)^{173}+40(V_{f})^{10} \tag{6}\]  
\[\eta_{11}=\frac{\left(\frac{E_{f}}{E_{m}}-1\right)}{\left(\frac{E_{f}}{E_{m}} +\xi_{11}\right)} \tag{7}\]  
\[\eta_{22}=\frac{\left(\frac{E_{f}}{E_{m}}-1\right)}{\left(\frac{E_{f}}{E_{m}} +\xi_{22}\right)} \tag{8}\]  
\[\eta_{11}=\frac{\left(\frac{G_{f}}{G_{m}}-1\right)}{\left(\frac{G_{f}}{G_{m}} +\xi_{12}\right)} \tag{9}\]  
Furthermore, in this study, a finite element analysis was performed through the homogenization technique using ANSYS Material Designer. ANSYS Material Designer is a module that enables material design and analysis by modeling composite materials or micromaterials per unit square. Through this module, a finite element analysis was performed by modeling the composite material. This was accomplished by setting the volume fraction of fibers per unit volume to 5 VF% using the homogenization technique. Homogenization techniques have received increasing attention over the past decades for predicting the mechanical properties of composite materials. This is because homogenization techniques can efficiently quantify the interplay between microscopic and macroscopic properties [35; 36; 37; 38; 39; 40; 41]. In this study, the UHMWPE fiber was assumed to be a cylinder to predict the elastic properties of the composite material. It was modeled such that the UHMWPE fiber could be randomly arranged inside the Representative Volume Element (RVE) according to the aspect ratio.