# Modeling Shearing and Bending Behavior of Kiwifruit Branches Using the Discrete Element Method
## 3 Results and Discussion
### Screening Out Significant Parameters  
The scheme and results of the Plackett-Burman test are shown in Table 4. Six blank columns were created for error analysis, and a total of 12 tests were performed. As we can see from the results, the elastic modulus and shear strength varied in a wide range under different parameter combinations. The range of shear strength ranged from 12.17 to 66.15 MPa, while the elastic modulus ranged from 1.06 to 2.00 GPa.  
The results, as listed in Table 5, were analyzed using Design-Expert software 10 (Stat Ease Ltd., Godward St NE, Minneapolis, MN, USA). Both models demonstrated significance with \(p\)-values lower than 0.05. In terms of shear strength, the cohesion of the bond and the effective modulus between the ball and the wall were found to be significant factors. This relation between cohesion and shear strength was also found in an experiment on frozen unsaturated silt [26]. Study [27] reported a significant effect of cohesion on tensile strength, indicating the importance of cohesion on the DEM model. Similarly, the effective modulus of the bond, the effective modulus between the ball and the wall, and the normal-to-shear stiffness ratio were identified as influential on the elastic modulus. However, the effective modulus of the ball and the tensile strength of the bond did not exhibit a significant impact on either of the mechanical properties assessed.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & **A** & **B** & **C** & **D** & **E** & **F** & **Shear Strength (MPa)** & **Elastic Modulus (GPa)** \\ \hline
1 & 1 & \(-1\) & \(-1\) & \(1\) & \(1\) & \(1\) & \(58.20\) & \(1.21\) \\
2 & 1 & \(-1\) & \(1\) & \(-1\) & \(-1\) & \(1\) & \(14.63\) & \(1.03\) \\
3 & \(-1\) & 1 & \(-1\) & \(1\) & \(1\) & \(-1\) & \(63.46\) & \(2.00\) \\
4 & 1 & \(-1\) & \(1\) & \(-1\) & \(1\) & \(-1\) & \(39.67\) & \(1.42\) \\
5 & \(-1\) & 1 & \(-1\) & \(1\) & \(-1\) & \(1\) & \(16.42\) & \(1.44\) \\
6 & 1 & \(-1\) & 1 & \(1\) & \(-1\) & \(-1\) & \(30.55\) & \(1.21\) \\
7 & \(-1\) & \(-1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(66.15\) & \(1.03\) \\
8 & \(-1\) & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & \(27.11\) & \(1.53\) \\
9 & 1 & 1 & 1 & 1 & 1 & 1 & \(57.34\) & \(1.57\) \\
10 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(14.03\) & \(1.17\) \\
11 & \(-1\) & 1 & \(-1\) & \(-1\) & \(1\) & \(1\) & \(38.78\) & \(1.73\) \\
12 & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(12.17\) & \(1.55\) \\ \hline \end{tabular}
\end{table}
Table 4: Scheme and results of Plackett–Burman design test.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Mechanical Properties** & **Max** & **Min** & **Average** & **Standard Deviation** \\ \hline External diameter (mm) & 13.5 & 8.1 & 10.5 & 1.4 \\ Inner diameter (mm) & 4.5 & 1.6 & 3.0 & 0.7 \\ Shear strength (MPa) & 20.37 & 49.78 & 31.38 & 6.72 \\ Elastic modulus (GPa) & 1.79 & 0.72 & 1.21 & 0.34 \\ \hline \end{tabular}  
* Max: the maximum value of the samples that has been tested; Mir: the minimum value of the samples that has been tested.  
\end{table}
Table 3: Mechanical properties of kiwifruit branch.