## 1 Introduction  
Due to their excellent mechanical strength, thermal conductivity, and electrical conductivity, carbon nanotubes (CNTs) are widely used in various industries, including the aerospace, defense, automotive, and athletic industries [1]. In CNT-based nanocomposites, CNTs are used as reinforcements to enhance the strength and stiffness of nanocomposites [2]. To apply these nanocomposites to structural designs, their mechanical properties must be well developed [3, 4].  
Numerical simulation methods such as finite element analysis is used due to the large costs involved in typical experimental methods for determining the mechanical properties of composites [5, 6, 7, 8, 9]. Among these methods, the representative volume element (RVE), which represents the geometric distribution of materials that are mixed in a composite, is extensively applied, and many studies have been performed using this approach [10, 11, 12, 13, 14, 15, 16, 17, 18]. For example, [PERSON] et al. [19] calculated and evaluated the effective properties of a square RVE considering CNT single filaments. [PERSON] et al. [20] defined RVEs based on square- or hexagonal-packed arrays containing CNT single filaments in the RVEs and reduced the analysis time using parallel arrangements. Further, [PERSON] et al. [21] modeled cylindrical RVEs containing CNT single filaments and analyzed their effective propertiesaccording to the variations in the volume fraction, aspect ratio, and orientation of the CNTs. However, the aforementioned studies only investigated RVEs in which extremely simple CNT single filaments were applied.  
Moreover, due to their highly complex internal structures resulting from the complex microstructures and dispersion of CNTs, it is difficult to assess the properties of CNT-based nanocomposites. To solve this problem, [PERSON] et al. [22] modeled and analyzed RVEs to investigate the effects of the modulus of elasticity on the CNT shape and dispersion state of the CNT-polyethylene composites. [PERSON] et al. [23] proposed 2D and 3D RVE approaches to identify the effects of nonlinear compressive responses according to the CNT orientation, CNT volume fraction, and CNT aspect ratio of CNT/epoxy nanocomposites. [PERSON] et al. [24] proposed a computational homogenization algorithm that can be used to define the RVE for CNT polymer composites. However, no studies have yet developed criteria for defining whether an RVE represents the internal structure of the nanocomposite (e.g., RVE size). To select an appropriate RVE, it is necessary to identify the main variables with the greatest influence on the effective properties of RVEs and to determine the mechanism through which they act.  
This study investigated the main variables affecting the effective properties of the RVEs of nanocomposites consisting of unidirectionally aligned CNTs, and analyzed the mechanism through which they act. For this purpose, in Section 2, MWNTs and polyvinylidene fluoride (PVDF) were selected as the components of the nanocomposites, and the main variables were selected considering the variations in the effective properties. Then, in Section 3, using the geometrical relationship between the RVE and CNT lengths considering the main variables, a simplified two-parameter equation that can be used to calculate the effective properties of the RVE was derived. In Section 3, a Monte Carlo simulation was conducted to examine the irregularity of the CNT length, which is one of the main variables, and the suitability of the simplified two-parameter approach for predicting the effective properties of RVE was verified. Finally, Section 4 presents the conclusions of this study.