# Finite Element Simulation of the Flat Crush Behavior of Corrugated Packages
## 3 Results and Discussion
### Comparison with the Experimental Study  
Figures 7 and 8 present the SS curves of the corrugated paperboard (circular specimens of \(\Phi\)90.6 mm [19]) by flute type analyzed through experiments, as well as using FEA. In the case of SW-A/F, the SS curves obtained through the experiment and FEA were in good agreement within a compressive strain of approximately 45%. However, in the case of SW_B/F and DW_BB/F, the SS curves between the two methods of the experiment and FEA were well matched in the initial elastic region, but from a compressive strain of approximately 6.5% or more, the SS curve through the FEA increased more steeply than that through the experiment. The difference between the experimental and FEA results for each flute type can be substantially reduced by applying viscoelastic properties to the paperboard during FEA. However, the difference in the SS curves for each flute type by FEA shows the same trend as in the experiment. Therefore, a qualitative analysis of the flat crush behavior for each flute type is possible with the FEA method used in this study. Figure 6: SS curves of the DW corrugated paperboard obtained using FEA. Figure 7: Comparison of the SS curves of the SW corrugated paperboard acquired through experiments and FEA. As shown in Figure 8, which shows the SS behavior according to the compression direction of DW-AB/F, the difference in the compression direction obtained by the experiment was very similar to that obtained by the FEA. The compression direction between the two methods exhibited no difference within a compressive strain of 60%. Table 5 presents the deformation process of the flute shape when the flat crush test was performed on the specimen of the corrugated paperboard. In the case of SW (A/F, B/F), the shape of the flute changed in the order of half-sine wave, trapezoid, square, and \(\Omega\) shape, similar to the FEA results presented in Table 4. This is because the horizontal movement of the upper and lower surfaces of the specimen was suppressed by sandpaper during the experiment and by the restraints of the nodes during the FEA. The flat crush behavior of the DW corrugated paperboard is shown by the interaction between two flutes, which are usually made of the same paperboard. In the case of AB/F, A/F with a large flute height and wavelength undergoes more deformation than B/F, and eventually collapses. Subsequently, the body loses resistance to compressive loads and undergoes plastic deformation. Therefore, the resistance of A/F determines the  
Figure 8: Comparison of the SS curves of the DW corrugated paperboard acquired through experiments and FEA. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Flute Type**} & \multicolumn{5}{c}{**Compressive Degree of the Modeled Test Specim**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline A/F & & & & & & \\ B/F & & & & & & \\ \hline AB/F & & & & & & \\ (B/F\(\rightarrow\)A/F) & & & & & & \\ AB/F & & & & & & \\ AB/F & & & & & & \\ AB/F & & & & & & \\ AB/F & & & & & & \\ (A/F\(\rightarrow\)B/F) & & & & & & \\ \hline BB/F & & & & & & \\ (\(\alpha=180^{\circ}\)) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Flat crush process of modelled test specimen by flute type through experiment. total amount of flat crush deformation before the collapse of the DW-AB/F corrugated paperboard. Meanwhile, in the case of DW-BB/F with a phase difference of 180\({}^{\circ}\), where the top and flute bottom of the upper and lower flutes are in direct contact, the two flutes are deformed almost simultaneously and support the deformation and load together, similar to the FEA results. Tables 4 and 5 present FEA and experimental results, respectively, of the analysis with the constrained horizontal translation motion of the top and bottom surfaces of the (modeled) test specimen. If they were not constrained (i.e., sandpaper was not used for testing and friction contact conditions were provided for FEA), the specimens were compressed occasionally while being pushed in one direction.