# Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing
## 4 Analysis and Discussion  
### Mathematical Model of Energy Absorption Efficiency  
Energy absorption (EA) is the total energy obtained from a load-displacement curve. As the evaluation zone of EA, we selected the displacement range between 0 and 60 mm, where the load had been generated in the experiment. EA is represented by Expression (1), where F is generated load, and s is displacement. \[\text{EA}=\int_{0}^{60}F.ds \tag{1}\]  
Figure 14: Nonprogressive crushing procedures of compression test (case: 16 ply-P5). Figure 13: Progressive crushing procedures of compression test (case: 12 ply-P15). Figure 15: Comparison of specimen after compression test. (**a**) Progressive crushing, case: 12 ply-P15; (**b**) nonprogressive crushing, case: 16 ply-P5. Energy absorption efficiency (EAE) is defined as the obtained value by dividing EA until 60 mm of the specimen becomes deformed by mass m of the deformed 60 mm portion of a corrugated structure pert. This is represented by Expression (2). The value of EAE is large when efficiency is high. \[\text{EAE}=\frac{EA}{m} \tag{2}\]  
Figure 16 shows the relation between EAE and the pitch with the varied numbers of stacks. As shown in Figure 16, EAE mostly linearly decreased with the increase in pitch in each number of stacks, except for 16 ply-P5. EAE increased with the increase in the number of stacks. Multiple regression analysis was conducted, with the number of stacks and pitch serving as explanatory variables and EAE as a response variable. Table 3 shows the explanatory variables and response variable. Figure 16: EAE–pitch curves. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Explanatory Variable**} & \multicolumn{2}{c}{**Response Variable**} \\ \hline \hline \multicolumn{2}{c}{**Number of Stacks (ply)**} & **Pitch (mm)** & **EAE (J/g)** \\ \hline \multirow{5}{*}{8} & 5 & 51.3 \\ \cline{2-3}  & 10 & 47.0 \\ \cline{2-3}  & 15 & 47.1 \\ \cline{2-3}  & 20 & 45.3 \\ \hline \multirow{5}{*}{12} & 5 & 62.1 \\ \cline{2-3}  & 10 & 56.0 \\ \cline{2-3}  & 15 & 54.8 \\ \cline{2-3}  & 20 & 51.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Explanatory variable and response variable (EAE). Multiple regression analysis was conducted on all experiment results and only on those that resulted in progressive crushing mode. For EAE, a linear model was used because the relation between the number of stacks and pitch mostly linearly varied. The model expression is represented by Expression (3). \[\text{EAE}=\beta_{0}+\beta_{1}\text{S}+\beta_{2}\text{P} \tag{3}\]  
where S is the number of stacks, P is pitch, \(\beta_{0}\) is intercept, \(\beta_{1}\) is partial regression coefficient of the number of stacks, and \(\beta_{2}\) is partial regression coefficient of the pitch. Table 4 shows the multiple regression analysis results conducted on all experiment results. Results were considered to be statistically significant when the \(p\) value was below 0.05. In this model, since the \(p\) value of the pitch was larger than 0.05, and 0 was included in the 95% confidence interval, the response variable was not explained by the explanatory variables. To improve prediction accuracy, multiple regression analysis was conducted by excluding the experimental results of 16 ply-P5, which had not resulted in progressive crushing mode. Table 5 shows the multiple regression analysis results excluding 16 ply-P5 experimental results.