*3.3. Calibration of the Contact Parameters between Phloem and Xylem* 3.3.1. Phloem–Xylem Restitution Coefficient

The physical test result shows that the average maximum rebound height of the ramie xylem on the phloem was 21.3 mm. In the discrete element simulations, to avoid interference, all contact parameters, except the restitution coefficient between the xylem and phloem, were set to 0. After the presimulation tests, the restitution coefficient between the xylem and phloem ranged from 0.4 to 0.7. The simulation test design for the restitution coefficient is shown in Table 4. Three repetitions were conducted for each group, and the mean value was taken.


**Table 4.** Simulation test results for the restitution coefficient between xylem and phloem.

The simulation test results in Table 4 were plotted as a scatter plot and fitted. The fitted curve obtained is shown in Figure 11. The fitting equation for the coefficient of restitution between the ramie xylem–phloem (*e*1) and the maximum rebound height (*h*max) is shown in Equation (5):

$$h\_{\max} = 45.91 - 187e\_1 + 244.5e\_1^2 \tag{5}$$

where *h*max represents the maximum rebound height, in millimeters; *e*<sup>1</sup> represents the coefficient of restitution between the phloem and the xylem.

**Figure 11.** Fitted curve of the restitution coefficient and maximum rebound height.

The determination coefficient (R2) of the fitting equation is 0.996, indicating the high reliability of the fitting equation. By substituting the measured maximum rebound height into Equation (5), *e*<sup>1</sup> is calculated as 0.60. Using the coefficient of restitution (*e*1) for the simulation tests, repeating five times, and taking the average value, the maximum rebound height is 20.85 with an error of 2.11%. The results show that the simulation results after the calibration are consistent with the physical test results. Therefore, the coefficient of restitution between the ramie phloem and xylem was determined to be 0.60.

#### 3.3.2. Phloem–Xylem Static Friction Coefficient

The coefficient of the static friction (*μ*s) between the ramie phloem and xylem was determined by measuring the average sliding angle of the xylem on the phloem's surface during inclined plane sliding. The physical test result shows that average sliding angle between the phloem and xylem was measured to be 31.61◦. In the DEM simulation test, the coefficient of restitution was set to the calibrated value, and the range of the coefficient of the static friction was set to 0.1 ~ 0.7 with an interval of 0.1. The remaining contact parameters were all set to 0. The simulation test of the static friction coefficient is shown in Table 5. Each group of tests was repeated three times, and the average value was acquired to obtain the relationship between the sliding angle and the static friction coefficient.

**Table 5.** Simulation test results for the static friction coefficient between the xylem and phloem.


The simulation test results were plotted as a scatter plot and fitted, and the fitting curve is shown in Figure 12. The fitting equation for the static friction coefficient between the ramie phloem–xylem (*μ*s) and the sliding angle (α) is shown in Equation (6):

$$
\mu = 1.393 + 72.01 \mu\_s - 28.44 \mu\_s^{-2} \tag{6}
$$

where *α* is the sliding angle in degrees, ◦; and *μ*<sup>s</sup> is the static friction coefficient between the phloem and xylem.

The fitting results show that the determination coefficient (R2) of the fitting equation is 0.996, indicating that the reliability of the fitting equation is high. By substituting the measured sliding angle into Equation (6), *μ<sup>s</sup>* is calculated to be 0.53. A simulated verification test was performed, and the average sliding angle was obtained by repeating the test five times, which was 31.54◦. The relative error between the simulated and physical test results was 0.22%, indicating that the calibrated simulation results are consistent with the physical test results. Therefore, the coefficient of the static friction between the ramie phloem and xylem was determined to be 0.53.

**Figure 12.** Fitting curve of the static friction coefficient and sliding angle.
