## 1 Introduction  
Fuel cells are electrochemical devices that convert chemical energy directly into electrical energy. There are various types such as proton-exchange membrane fuel cells (PEMFCs), solid oxide fuel cells (SOFCs) and molten carbonate fuel cell (MCFCs) depending on fuel and substances. Among them, PEMFCs are the most attractive fuel cells due to their low operating temperature, compact structure and fast startup and shutdown facilities [1; 2; 3; 4]. In terms of structural and functional aspects, the fuel cell can be divided into a separation plate, a gas diffusion layer (GDL), a membrane electrode assembly (MEA) and a gasket. The porous structure of a GDL transfers the reactant gas (hydrogen and oxygen) supplied through the separator to the MEA where the electrochemical reaction occurs and discharges the water generated by the electrochemical reaction to the separator in the catalyst layer of the MEA. There are many pores in the GDL that are the passages of the reaction gas and the generated water. Through these numerous pores, the gases (hydrogen and oxygen) are transported, and the water produced by the electrochemical reaction is discharged [5; 6]. The porous structure of the GDL typically consists of a thin layer of carbon fiber paper, carbon cloth or nonwoven. The GDL plays an important role that determines the performance of the fuel cell. Recently, in order to improve the efficiency of the flow characteristics inside the GDL, various studies have been carried out from the viewpoint of the design such as the clamping pressure that is produced in the stack assembly process, the assembling method and the optimum structural design method [7,8]. These studies aim to control the material characteristics and the design variables of fuel cells, such as hydrophobic polymer content [9,10], pore-size distribution [11,12], temperature distribution [13], humidity, differential pressure effects and compressive force effects of GDLs [14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. The amount of compression ratio of the GDL affects the porosity, directionality and the fraction of the pore space occupied by liquid water and affects the performance of a fuel cell. For example, [PERSON] et al. [24] studied porosity characteristics of the composite porous GDLs due to manufacturing variations in the manufacturing process. [PERSON] et al. [25] studied alternative methods to control the compression ratio according to the design of the stack structure and thickness of the gasket. [PERSON] et al. [26] predicted the pore structure according to the direction and geometrical changes of GDL structure by compression load and then investigated the change of internal flow characteristics. [PERSON] et al. [27] performed computational fluid dynamics (CFD) analysis on the intrusion effect of the gas diffusion layer pushing into the channel, due to the compressive force of the separator and the deterioration of the cell performance due to the thickness reduction of the GDL itself. Most of the above studies are mostly for predicting the changes in GDL flow characteristics and fuel cell performance due to the compressive force. Especially in order to analyze the performance of the fuel cell, it is essential to identify the physical properties of the GDL. Since these properties vary greatly depending on the compression ratio, it is necessary to study the prediction of GDL properties depending on the compression ratio. For GDL tissues, both chemical and mechanical stability should be satisfied [28]; the prediction of effective mechanical properties of the GDL can give us the ability to consider the orientation of the material stacking during the stack assembling process and manufacturing standard for the compressive clamping load. Several types of homogenization methods have been studied to predict the equivalent material properties of composite materials on the information for microstructure, such as mean field and full field approaches. Within the mean field approach, bounding and estimating methods can be distinguished [29].