# Modeling Shearing and Bending Behavior of Kiwifruit Branches Using the Discrete Element Method
## 3 Results and Discussion
### Parameter Verification and Simulation of Shearing and Bending Process  
Based on the above response surface test analysis, a multi-objective variable optimization method facilitated by Design-Expert software was employed to identify the optimal values that minimize the relative error for both indices. By setting the experimental outcomes as the benchmark, the analysis revealed that the optimal values were \(2.2\times 10^{9}\) Pa for the effective modulus of the bond, \(2.56\times 10^{8}\) Pa for the cohesion of the bond, \(1.27\times 10^{8}\) Pa for the effective modulus between the ball and the wall, and \(1.16\) for the normal-to-shear stiffness ratio. Subsequently, these optimal combinations were integrated into the DEM model to verify the results. With the derived values, a verification simulation test was performed. The simulation result of the shear strength was \(29.57\) MPa and the elastic modulus was \(1.17\) GPa. The discrepancies between these results and the experimental data were \(5.8\%\) and \(3.3\%\), respectively. The relative error was calculated to be \(4.5\%\), which is lower than the previous result. According to previous DEM model establishment studies, an error within \(10\%\) is acceptable [30; 31]. Therefore, the calibrated parameters for the kiwifruit branch model were deemed reliable. As depicted in Figure 7a, the force-displacement curves from both the experimental shear tests and the simulations were found to be largely consistent. The shear force increased initially, reaching a peak at about \(6\) mm of displacement. It then slightly decreased before increasing again with minor fluctuations until it reached the maximum shear force. Subsequently, the force dropped sharply, aligning with the behavior observed in shearing tests of banana straw, Chinese cabbage root, and safflower [32; 33; 34]. However, two peak points were found in the shearing simulation of Chinese cabbage simulation due to the lower density of the model. Additionally, the shear force of safflower slowly decreased after the peak point because it is more flexible than the kiwifruit branch. In the simulation of the shearing process (Figure 8), at first, the central part of the branch, positioned within the upper blade of the shearing fixture, underwent extrusion, and the junction between the central section and the two ends was subjected to tensile forces (Figure 8a). As the load increased, the right junction experienced failure, causing the branch to separate into two segments (Figure 8b). Subsequently, with the ongoing application of load, the left junction also failed, ultimately resulting in the branch breaking into three distinct pieces (Figure 8c). These outcomes displayed high resemblance with those observed during the experiment (Figure 8d), indicating the visual simulation ability of the DEM. This kind of ability was also found in the simulation of a series of agricultural materials, such as wheat plants, maize straw, Chinese cabbage, and tobacco leaf [32; 35; 36; 37]. Figure 7: Displacement–force curve comparison of laboratory and simulation test: (**a**) displacement–force curve on shearing test, (**b**) displacement–force curve on three-point bending test. As observed in Figure 7b, the force-displacement curves from both the experimental and simulated three-point bending tests closely resembled each other. At the initial stage, with a low load, the branch sample and the DEM model exhibited elastic behavior, characterized by a rapid increase in bending force. As the loading cylindrical indenter continued to move, the rate of force increase diminished, and the curve's slope decreased, indicating the onset of plastic behavior--a phenomenon also observed in wheat straw [21,38]. During the bending process, as illustrated in Figure 9a, the bottom section of the branch experienced tensile stress, while the upper section was under compressive stress. The greatest displacement occurred in the middle and bottom sections of the branch, leading to initial fracture at the bottom (Figure 9b).