## 2 Materials and Methods
### Material Parameter Calibration
#### 2.3.3 Coefficient of Restitution Determination  
The coefficient of restitution (COR), serving as a core parameter for evaluating an object's ability to recover its original configuration after collision, holds a pivotal position in the study of collision dynamics within multibody systems [17]. It is defined as the ratio of the normal relative velocity of the objects along the contact interface before and after collision [18], specifically the ratio of the separation velocity after collision to the approach velocity before collision. Based on this definition, the mathematical expression for the coefficient of restitution is formulated as follows:  
\[e=\frac{|v_{2}|}{|v_{1}|} \tag{4}\]  
where \(v_{1}\) and \(v_{2}\) denote the velocities of the experimental material before and after the collision, respectively. Based on the kinematic principles of free fall, the velocities before and after the collision can be calculated using the following equations:  
\[v_{1}=\sqrt{2 gh_{1}} \tag{5}\]  
\[v_{2}=\sqrt{2 gh_{2}} \tag{6}\]  
In the equation, \(h_{1}\) represents the initial drop height of the material before collision, and \(h_{2}\) denotes the vertical distance from the collision plane to the highest point reached by the material after rebounding. Consequently, the final expression for the coefficient of restitution is formulated as:  
\[e=\sqrt{\frac{h_{2}}{h_{1}}} \tag{7}\]  
This study employed the free-fall experimental method [19], with the experimental principle illustrated in Figure 14. The rebound heights of raisins and various foreign objects after collision were measured using a height gauge, with 304 stainless steel plates, raisins, stems, branches, stones, plastics, and other materials serving as experimental contact base plates. To ensure data reliability, raisin particles were freely released from a fixed height \(h_{1}=150\) mm, and the entire process was recorded by a high-speed camera in a plane perpendicular to the falling direction, as shown in Figure 14. Each experimental group was repeated 10 times, and the maximum rebound height of raisin particles was recorded to calculate the mean value \(h_{2}\). Finally, the COR for raisins and various foreign objects were determined using the COR calculation formula. The COR values were as follows: 0.48 for raisin-raisin collisions, 0.32 for raisin-stem/branch collisions, 0.44 for raisin-stone collisions, 0.35 for raisin-plastic collisions, 0.53 for raisin-304 stainless steel collisions, 0.20  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Dimension Parameter** & **Raisin** & **Stem** & **Branch** & **Stone** & **Stone** \\ \hline Length (mm) & 19.82 \(\pm\) 1.85 & 8.61 \(\pm\) 0.83 & 22.32 \(\pm\) 6.73 & 3.87 \(\pm\) 1.04 & 8.24 \(\pm\) 1.24 \\ Breadth (mm) & 7.64 \(\pm\) 1.24 & 1.27 \(\pm\) 0.43 & 2.02 \(\pm\) 1.24 & 3.87 \(\pm\) 1.04 & 4.39 \(\pm\) 0.64 \\ Height (mm) & 6.32 \(\pm\) 1.02 & 1.27 \(\pm\) 0.43 & 2.02 \(\pm\) 1.24 & 3.21 \(\pm\) 0.56 & 2.47 \(\pm\) 0.34 \\ Weight (g) & 1.32 \(\pm\) 0.21 & 0.11 \(\pm\) 0.04 & 3.17 \(\pm\) 0.33 & 3.27 \(\pm\) 0.31 & 1.97 \(\pm\) 0.31 \\ \hline \end{tabular}
\end{table}
Table 5: Physical property parameters of materials.  
for stem/branch-stem/branch collisions, 0.36 for stem/branch-stone collisions, 0.35 for stem/branch-plastic collisions, 0.47 for stem/branch-304 stainless steel collisions, 0.50 for stone-stone collisions, 0.45 for stone-plastic collisions, 0.63 for stone-304 stainless steel collisions, 0.46 for plastic-plastic collisions, and 0.50 for plastic-304 stainless steel collisions.