# Modeling Shearing and Bending Behavior of Kiwifruit Branches Using the Discrete Element Method
## 3 Results and Discussion
### Determination of Optimal Values for the DEM Parameters
**} & \multicolumn{5}{c}{**Test Factors**} & \multirow{2}{*}{**Shear Strength (MPa)**} & \multirow{2}{*}{**Elastic Modulus (GPa)**} \\ \cline{2-2} \cline{5-6}  & **B** & **D** & **E** & **F** \\ \hline
1 & \(2\times 10^{9}\) & \(1\times 10^{8}\) & \(2.6\times 10^{8}\) & 1.0 & 34.98 & 1.24 \\
2 & \(2.2\times 10^{9}\) & \(1.8\times 10^{8}\)  
Figure 6a illustrates that the elastic modulus obviously increased with the simultaneous increase in effective modulus between ball and wall and effective modulus of bond. Whereas a more modest increase was observed when either the effective modulus between the ball and wall or the effective modulus of the bond was increased. As shown in Figure 6b, with the increase in the effective modulus between the ball and wall and cohesion, the shear strength increased. This is similar to the findings of a DEM maize straw model study [28], where the maximum shear force was found to increase with the increase in stiffness between ball and wall. Additionally, the positive effect of cohesion was also found on tensile strength [29]. The curve for the effect of the effective modulus between the ball and wall was steeper than that for cohesion, indicating that the former has a greater influence on shear strength than the latter. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**y\({}_{1}\): Elastic Modulus (GPa)**} & \multicolumn{4}{c}{**y\({}_{2}\): Shear Strength (MPa)**} \\ \cline{2-10}
**Source** & \begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **df** & \begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & \begin{tabular}{c} **\(p\)-Value** \\ \end{tabular} & **\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **df** & \
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** &
\begin{tabular}{c} **F-Value** \\ \end{tabular} \\ \hline Model & 0.374 & 14 & 0.027 & 21.8 & 0.00 & 3850.913 & 14 & 275.065 & 12.6 & 0.00 \\ B & 0.053 & 1 & 0.053 & 43.2 & 0.00 & 22.909 & 1 & 22.909 & 1.1 & 0.34 \\ D & 0.008 & 1 & 0.008 & 6.8 & 0.04 & 330.352 & 1 & 330.352 & 15.2 & 0.01 \\ E & 0.105 & 1 & 0.105 & 85.5 & 0.00 & 2862.918 & 1 & 2862.918 & 131.6 & 0.00 \\ F & 0.010 & 1 & 0.010 & 8.1 & 0.03 & 0.482 & 1 & 0.482 & 0.0 & 0.89 \\ BD & 0.000 & 1 & 0.000 & 0.4 & 0.56 & 6.631 & 1 & 6.631 & 0.3 & 0.60 \\ BE & 0.001 & 1 & 0.001 & 0.4 & 0.53 & 18.503 & 1 & 18.503 & 0.9 & 0.39 \\ BF & 0.003 & 1 & 0.003 & 2.5 & 0.17 & 3.061 & 1 & 3.061 & 0.1 & 0.72 \\ DE & 0.004 & 1 & 0.004 & 3.1 & 0.13 & 48.154 & 1 & 48.154 & 2.2 & 0.19 \\ DF & 0.000 & 1 & 0.000 & 0.4 & 0.55 & 23.536 & 1 & 23.536 & 1.1 & 0.34 \\ EF & 0.001 & 1 & 0.001 & 0.8 & 0.40 & 6.588 & 1 & 6.588 & 0.3 & 0.60 \\ B\({}^{2}\) & 0.000 & 1 & 0.000 & 0.0 & 0.88 & 0.322 & 1 & 0.322 & 0.0 & 0.91 \\ D\({}^{2}\) & 0.054 & 1 & 0.054 & 44.4 & 0.00 & 25.041 & 1 & 25.041 & 1.2 & 0.32 \\ E\({}^{2}\) & 0.021 & 1 & 0.021 & 17.2 & 0.01 & 108.858 & 1 & 108.858 & 5.0 & 0.07 \\ F\({}^{2}\) & 0.000 & 1 & 0.000 & 0.3 & 0.61 & 31.330 & 1 & 31.330 & 1.4 & 0.28 \\ Lack of & & 0.007 & 2 & 0.004 & & & 130.528 & 2 & 65.264 & & \\ Fit & & & & & & & & & & \\ Pure & 0 & 4 & 0 & & & & & & & \\ Error & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Variance analysis of response surface test. Figure 6: Response surface of the two significant factors on mechanical response: (**a**) response surface on elastic modulus and (**b**) response surface on shear strength.