## 2 Materials and Methods
### FE Modeling and Analysis Procedures  
The finite element (FE) model was created based on the physical specifications (Table 1) of the two single-wall (A/F and B/F) and two double-wall (AB/F and BB/F) corrugated paperboards used during the ECT test. The geometrical shape of the flute was modeled as a cosine function. According to [PERSON] et al. [7], the phase angle between two flutes (having the same flute type) did not significantly affect the buckling strength during edgewise compression using the double-wall corrugated paperboard. Therefore, the FE model for the test specimens made of BB/F was built by aligning the flute tops and flute bottoms with a phase shift of 0.5\(\lambda\) and 180\({}^{\circ}\) (Table 1). The connection point between the liner and flute of the corrugated paperboard was modeled using a sharing method for the point (nodes) for simplification. The allowable gap between surfaces was given by assigning pinball regions to raise the convergence in the case of large deformations. The shape of the specimen was defined in KS M 7063-1 method A [13], TAPPI T 838 [14], and FEFCO No.8 standards [15], respectively. The FE model used SOLID187 element for KS M 7063-1 method A and TAPPI T 838; SOLID186 element for FEFCO No.8 [33]. The models were meshed to produce 21,800 (A/F)-53,916 (BB/F) finite elements for KS M7063-1 method A, 10,064 (A/F)-24,027 (BB/F) finite elements for TAPPI T 838, and 5356 (B/F)-13,020 (AB/F) finite elements for FEFCO No.8, while the total number of nodes was 44,993 (A/F)-104,256 (BB/F) for KS M7063-1 method A, 21,242 (A/F)-47,202 (BB/F) for TAPPI T 838, and 38,838 (B/F)-85,356 (BB/F) for FEFCO No.8. Figures 4 and 5 show examples of the meshed FE models for A/F and AB/F corrugated paperboard prepared following the requirements of each standard. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Components**} & \multirow{2}{*}{\begin{tabular}{c} **Thickness** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Wavelength** \\ **(\(\lambda\)) (mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Height of Flute** \\ **(\(\lambda\)) (mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Take-Up** \\ **Factor** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Flutes per** \\ **300 mm Liner** \\ \end{tabular} } \\ \hline \multirow{2}{*}{Flute} & A/F & 0.22 & \begin{tabular}{c} 9.00 \\ (8.33\(\rightarrow\)9.38) \\ \end{tabular} & 4.90 & 1.560 & 33 \\  & & & (4.5–4.8) & (1.6) & (34 \(\pm\) 2) \\ \cline{2-6}  & B/F & 0.22 & \begin{tabular}{c} 6.00 \\ (5.27\(\rightarrow\)6.25) \\ \end{tabular} & \begin{tabular}{c} 2.65 \\ (2.5–2.8) \\ \end{tabular} & \begin{tabular}{c} 1.424 \\ (1.4) \\ \end{tabular} & \
\begin{tabular}{c} 50 \\ (50 \(\pm\) 2) \\ \end{tabular} \\ \hline \multirow{2}{*}{Liner} &
\begin{tabular}{c} Inner \& \\ outer \\ \end{tabular} & 0.20 & & & & \\ \cline{2-6}  & Middle & 0.22 & & BB/F-DW: & & \\ \hline \hline \end{tabular}  
Notes: KS T 1034 [32].  
\end{table} 
Table 1: The measured specifications of the corrugated paperboards used in the study. Figure 4: The meshed 3D models for FE simulation of A/F corrugated paperboard; they should be listed as: (**a**) KS M 7063-1 method A; (**b**) TAPPI T 838; (**c**) FEFCO No.8. Before selecting the mesh size, the mesh convergence study was conducted to reassure that the employed mesh element size is neither time consuming nor leading to any discretization error. In this simulation, the mesh study includes five different element mesh sizes. Table 2 shows von Mises stress of different mesh size of A/F by KS M 7063-1 method A using FEA. It can be seen from Table 2 that stress is similar for the mesh size ranging from 1.3 to 1.7 mm. By considering the least number of distorted elements and the time taken to run the simulation, mesh size of 1.3 mm was chosen for the remaining study. The post-processor used for the study was ANSYS(r) FE [33].