## 2 Materials and Methods
### Material Properties  
The required material properties for FEA were [PERSON]'s modulus, Poisson's ratio, shear modulus, yield strength, and frictional coefficient between the corrugated paperboard components. The corrugated paperboard components such as liners and corrugated mediums were assumed to be orthotropic materials, which means their material properties have symmetricity for \(x\)(MD), \(y\)(CD), and \(z\)-plane (Figure 1). Therefore, each board had nine elastic material properties, such as \(E_{x}\), \(E_{y}\), \(E_{z}\), \(G_{xy}\), \(G_{xz}\), \(G_{yz}\), \(\mu_{xy}\), \(\mu_{xz}\), \(\mu_{yz}\), and two strength values, \(\sigma_{y\text{-MD}}\) and \(\sigma_{y\text{-CD}}\)[34].  
Among the material properties described above, the \(E_{x}\) and \(E_{y}\), in-plane Elastic moduli, and the \(\sigma_{y\text{-MD}}\) and \(\sigma_{y\text{-CD}}\) values were calculated using the load vs. elongation plots (Figure 6) of an uniaxial tensile test (tensile tester: KST, capacity: 100 kgf, extensometer resolution: 0.01 mm, max. tensile force of pneumatic grip: 2 kN) based on ISO 1924 [35].  
Based on the shape of the load vs. elongation plot, the stress-strain behavior of the liner and medium was assumed to be linear elastic to simplify the model. Due to the difficulty of measuring the other material properties as a result of the thickness of the paper, these material properties are typically estimated.  
The Poisson ratio of the material was obtained from Nordstrand [28], \(E_{z}\) out-of-plane elastic modulus was estimated using Equation (1) [36], and shear modulus was estimated using Equation (2) [4; 37]. The final material properties used for the FE model are presented in Table 3.  
\[E_{z}=E_{x}/200 \tag{1}\]  
\[G_{xy}=0.387\sqrt{E_{x}E_{y}},\ G_{xz}=E_{x}/55,G_{yz}=E_{y}/35 \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Paperboards**} & \multicolumn{3}{c}{**Young’s Modulus (GPa)**} & \multicolumn{3}{c}{**Poisson’s Ratio \({}^{1}\)**} & \multicolumn{3}{c}{**Shear Modulus (GPa)**} & \multicolumn{3}{c}{**Yield Strength (MPa)**} \\ \cline{2-13}  & \(E_{x}(E_{\text{MD}})\) & \(E_{y}(E_{\text{CD}})\) & \(E_{z}\) & \(\mu_{xy}\) & \(\mu_{xz}\) & \(\mu_{yz}\) & \(G_{xy}\) & \(G_{xz}\) & \(G_{yz}\) & \(\sigma_{y\text{-MD}}\) & \(\sigma_{y\text{-CD}}\) \\ \hline \multirow{2}{*}{K180} & 2.20 & 0.37 & \multirow{2}{*}{0.011} & \multirow{2}{*}{0.34} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.34} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.349} & \multirow{2}{*}{0.040} & \multirow{2}{*}{0.010} & \multirow{2}{*}{12.12} \\  & (\(\pm\)0.02) & (\(\pm\)0.01) & & & & & & & & & (\(\pm\)0.8) & (\(\pm\)0.1) \\ \hline \multirow{2}{*}{SK180} & 3.16 & 0.40 & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.435} & \multirow{2}{*}{0.057} & \multirow{2}{*}{0.011} & \multirow{2}{*}{0.250} & \multirow{2}{*}{19.50} \\  & (\(\pm\)0.07) & (\(\pm\)0.01) & & & & & & & & & & (\(\pm\)0.8) & (\(\pm\)0.5) \\ \hline \hline \end{tabular}  
Notes: The values in parentheses are standard deviation values. \({}^{1}\) [PERSON] [28].  
\end{table}
Table 3: Orthotropic material properties of corrugated paperboard components used for the FEA.  
Figure 6: Load vs. elongation plots for the corrugated paperboard components. (CD—cross direction, MD—machine direction).  
As the flute deformation in edgewise compression proceeded, the contact area between the flute and liner on the left and right portions of the shared nodes increased gradually. Accordingly, the frictional contact conditions at a portion where contact was expected were used to accurately analyze the edgewise compression behavior of corrugated paperboard. The static-frictional coefficients for various contact conditions between corrugated paperboard components were measured based on ISO 15359 [38] using a frictional test device reported by [PERSON] et al. [39]. Figure 7 shows the static-frictional coefficient used for the model.