## 1 Introduction  
Carbon fiber reinforced composites are extensively utilized in various industries including aerospace, defense, automotive, and sports, due to their high specific strength and specific stiffness and excellent fatigue resistance. These composites can be classified into unidirectional (UD) and woven composite materials. In particular, woven carbon/epoxy composites feature improved in-plane mechanical properties and impact resistance due to tow structure [1; 2; 3; 4; 5]. Consequently, woven carbon/epoxy composites are mainly used in industries instead of the UD composites. The design of structures using carbon fabric composites requires highly reliable mechanical properties. The homogenization technique is a numerical procedure in which a heterogeneous elastic media is converted into an equivalent model, which is energetically equivalent to the authentic heterogeneous media. For fiber reinforced composites, the homogenization technique assumes the composite structures are composed of a periodic microstructure as shown in Figure 1, and reduces to a unit cell problem [6; 7; 8]. Hence, the homogenization method is used to estimate the various mechanical properties of composite materials, which takes into consideration their constituents and microstructure [9; 10; 11]. For example, [PERSON] et al. [12] created four representative volume elements (RVEs) including square and hexagonal arrays that have different fiber orientations in UD composites. Furthermore, they predicted the effective properties by comparing the random sequential adsorption (RSA) algorithm developed in this study with the Halpin-Tsai and Mori-Tanaka homogenization techniques. [PERSON] et al. [13] modeled the RVEs by considering the fiber orientation and ply angle of carbon fiber reinforced plastics (CFRPs), predicted the effective properties based on cross-scale simulations, and compared them with the tensile test results. [PERSON] et al. [14] suggested the Integrated Computational Material Engineering framework implemented by the rule of mixture (ROM) to produce a unidirectional CFRP laminated structure, and compared the tensile tests and 3-point bending tests results with the simulation results. The abovementioned studies proposed various RVE models to predict the effective properties of the fiber level. However, these models have limitations because they do not consider the uncertainties of mechanical properties caused by the structural characteristics of the fiber-matrix composites and various inherent defects [15]. For this, [PERSON] et al. [16] identified the linear correlation of the effective and material properties using the Monte Carlo simulation (MCS) to consider the uncertainties of the properties of fiber and matrix. [PERSON] and [PERSON] [17] analyzed the material properties according to deviations based on the square RVEs including single cylindrical fibers. However, the abovementioned studies only investigated the fiber levels of UD composites with considerably simpler internal structural shapes than those of the fabric composites. Fabric composites are disadvantageous because it is difficult to evaluate the mechanical properties using the conventional homogenization techniques at the fiber level due to the complexity of the internal structure of the constituents. To overcome this, the structural characteristics of fabric composites should be considered by conducting multi-scale analyses to consider the tow level, which fiber and matrix are combined, and the higher level with the tow/matrix combination. [PERSON] et al. [18] predicted the mechanical behavior of different plain weave structures using the discrete homogenization approach for the fabric composites. [PERSON] et al. [19] developed a multi-level homogenization model to determine the effective properties of the woven glass/epoxy composite multilayer printed circuit board.