# Modeling the Kinematic Response of Rice under Near-Ground Wind Fields Using the Finite Element Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Tested Rice and Paddy Field

#### 2.2. Rice Biological Characteristics Measurements

#### 2.2.1. Agronomic

_{s}, spike length $\varsigma $, plant height $H$, culm length $L$, culm diameter $D$, and wall thickness $t$ at 0.1 m from the root and the leaf length ${L}_{l}$, leaf width ${W}_{l}$, and leaf angle ${\phi}_{l}$ of the upper three leaves (please refer to Table 2 and Figure 2a).

_{1}. Then, they were placed in an oven in paper envelopes and maintained at 105 °C for 30 min. Finally, they were dried at 75 °C to a constant weight and the dry weight m

_{2}was obtained. The moisture content can be calculated as follows:

#### 2.2.2. Mechanical Tests

^{2}; $\Delta l$ is the specimen deformation in m; and $l$ is the specimen gauge length in m. The true stress and strain can be corrected via Equations (2) and (3), respectively:

^{2}and ${l}_{0}$ is the instantaneous length of the specimen in m.

^{3}) was measured via the drainage method, where $V$ is the drainage volume and $m$ is the fresh weight of rice. Poisson’s ratio was retrieved from the literature. In summary, the RWRM material parameters involved are listed in Table 4.

#### 2.3. Finite Element Model of Single Rice Setup

^{2}. Through iterations of the above two steps, the rice responses under different wind speeds can be obtained.

#### 2.4. Wind-Induced Response Calculation and Validation

#### 2.4.1. Rice Displacement under Different Wind Speeds

#### 2.4.2. Critical Wind Speed

^{4}, which can be obtained with Equation (8):

## 3. Result

#### 3.1. Wind-Induced Kinematic Response of Rice

#### 3.2. Critical Wind Speeds of Four Different Rice Species

## 4. Discussion

## 5. Conclusions

- (1)
- The model could suitably predict the displacement range of rice in response to a horizontal wind field, with an average paired difference of 13.48 mm and an error value 42.46 mm, which means the model can predict the windward tilt angle of rice, with an average error of 5 degrees. This is beneficial for visually understanding the wind resistance of rice. A significant correlation at the 1% level between the simulated and measured displacements in the same time step helps to underpin the validity of the model;
- (2)
- The model could suitably predict the stress of rice, as evaluated via the CWS. The CWS of the four rice species was 3.57 m/s and its pairwise difference between this model and another existing high-impact model was 0.368 m/s on average. We found that the CWS is primarily affected by the condition of the rice culm, especially the Young’s modulus of the culm. The more robust the culm, the higher the CWS. The CWS is secondarily affected by rice leaves. The larger and heavier the rice leaves, the lower the CWS;
- (3)
- The rice’s yield has a negative correlation with its wind resistance. Larger and heavier rice leaves along with a lower Young’s modulus are instead conducive to increased rice yields. Both the displacement and CWS were mainly influenced by the physical properties, such as the Young’s modulus. A bigger displacement and lower CWS could result in a higher rice yield.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Rice sample one week after tassel (the red marks ①②③ are the intercepted parts of the mechanical test specimens corresponding in Table 3). (

**b**) WE-D series precision micro-controlled electronic universal testing machine, for conducting tensile and bending tests.

**Figure 3.**Model setup and calculation process: (

**a**) geometric model of single rice plant; (

**b**) fluid domains in the rice plant’s periphery; (

**c**) mesh; (

**d**) wind speed at the near point of the rice surface when the inlet wind speed was set as 4 m/s; (

**e**) boundary loads on rice under this wind field; (

**f**) von Mises equivalent stress of rice; (

**g**) a change in the posture of the rice.

**Figure 4.**Test layout. The number 1, 2 and 3 are used to indicate specific positions of tested rice.

**Figure 5.**The simulated and measured displacements (x-component) of rice culm at the height of 0.5 m at different inlet wind speeds in Figure 6. (

**a**) mean inlet wind speeds of 3.2 m/s; (

**b**) mean inlet wind speeds of 3.9 m/s; (

**c**) mean inlet wind speeds of 3.6 m/s.

**Figure 7.**(

**a**) Critical wind speeds for the main stems of each species under both models. The letter A stands for 19X, B for NJ, C for T1002, and D for J1002. (

**b**) FEM with GLM linear fit, where the equation is y = −0.268 (±0.166) + 0.979 (±0.042)x, with a Pearson’s r value of 0.987, R square of 0.975, and adjusted R square of 0.973.

**Figure 8.**Heat map of correlation coefficients for Pearson’s correlation analysis of rice indicators.

Species Name * | Abbr. | Rice Type | Rice Growth Period (Date of 2021) | |||
---|---|---|---|---|---|---|

Sowing | Tassel | Spike | Harvest | |||

19 Xiang | 19X | Conventional indica | 16 July | 28 September | 1 October | 3 November |

Nan Jing Xiang Zhan | NJ | 16 July | 26 September | 29 September | 3 November | |

Taiyou 1002 | T1002 | Triple hybrid indica | 11 July | 25 September | 28 September | 3 November |

Jifengyou 1002 | J1002 | 11 July | 30 September | 4 October | 3 November |

Species * | $\mathit{H}$/mm | $\mathit{L}$/mm | $\mathit{D}$/mm | $\mathit{t}$/mm | ${\mathit{L}}_{\mathit{l}}$/mm | ${\mathit{W}}_{\mathit{l}}$/mm | ${\mathit{\phi}}_{\mathit{l}}$/deg |
---|---|---|---|---|---|---|---|

19X | 1155.0 | 896.3 | 9.68 | 2.07 | 520.7 | 15.8 | 10.00 |

NJ | 1063.8 | 790.0 | 8.69 | 1.92 | 523.6 | 13.1 | 23.25 |

T1002 | 1135.0 | 851.3 | 9.81 | 1.81 | 504.2 | 13.6 | 31.08 |

J1002 | 1057.5 | 825.5 | 8.39 | 1.35 | 530.1 | 16.7 | 11.50 |

Test Type | Rice Part * | Four Species’ Average Specimen Cross-Sectional Areas (mm^{2}) | Gauge Length (mm) | Loading Speed (mm/min) |
---|---|---|---|---|

Uniaxial tensile | The 1st leaf | 4.98/3.65/3.77/5.28 | 60 | 2 |

The 2nd leaf | 3.99/2.87/3.05/4.25 | 60 | 2 | |

Culm | 8.00/9.34/10.38/14.67 | 30 | 20 | |

Three-point bending | Culm | 30.06/31.93/25.98/39.97 | 70 | 20 |

Properties * | Variables | Species | Parts | Value | Source |
---|---|---|---|---|---|

Young’s modulus | $E$ (GPa) | 19X | culm | 0.63 | Measured/calculated |

leaf | 0.72/0.60 | Measured/calculated | |||

NJ | culm | 0.63 | Measured/calculated | ||

leaf | 0.31/0.38 | Measured/calculated | |||

T1002 | culm | 0.59 | Measured/calculated | ||

leaf | 0.66/0.72 | Measured/calculated | |||

J1002 | culm | 0.56 | Measured/calculated | ||

leaf | 0.54/0.61 | Measured/calculated | |||

Density | $\rho $ (kg/m^{3}) | All | culm | 1046 | Measured/calculated |

leaf | 1026 | Measured/calculated | |||

Poisson’s ratio | $\mu $ (dimensionless) | All | culm | 0.30 | Referred [21,22] |

leaf | 0.28 | Referred [23,24] | |||

Air density | ${\rho}_{Air}$ (kg/m^{3}) | / | / | 1.18 | COMSOL built-in material library |

Aerodynamic viscosity | ${\mu}_{Air}$ (Pa·s) | / | / | 1.84 × 10^{−5} | COMSOL built-in material library |

Gravity acceleration | $g$ (m/s^{2}) | / | / | 9.78 | Constant |

Parameter | 1 | 2 | 3 | |||
---|---|---|---|---|---|---|

RWRM | Measured | RWRM | Measured | RWRM | Measured | |

Quantity | 87 | 87 | 87 | 87 | 87 | 87 |

Maximum(mm) | 179.51 | 190.75 | 181.10 | 199.29 | 122.41 | 227.76 |

Minimum(mm) | 0.06 | −2.85 | 0 | −5.69 | 0.07 | −2.85 |

Average(mm) | 76.80 | 74.19 | 75.71 | 56.05 | 52.37 | 70.55 |

Paired Difference(mm) | 2.61 | 19.66 | −18.17 | |||

Paired t-tests p ^{1} | 0.595 | 0.003 *** | 0.006 *** | |||

Cohen’s d | 0.058 | 0.330 | 0.303 | |||

Pearson’s p ^{1} | 0.480 *** | 0.560 *** | 0.321 *** |

^{1}p is the correlation coefficient, and *** means the concerning values were significant at the 1% level.

Species | Estimated Thousand Grain Weight (g) | Final Yield (g/50 Plants) | Bending Energy (mJ) | Culm Moisture Content (%) | Leaf Moisture Content (%) |
---|---|---|---|---|---|

19X | 21.4 | 1586.37 | 178.86 | 85.90 | 73.07 |

NJ | 21.7 | 1547.70 | 146.27 | 86.39 | 67.16 |

T1002 | 23.5 | 1648.43 | 132.45 | 87.02 | 70.12 |

J1002 | 26.5 | 2070.93 | 247.04 | 87.31 | 71.11 |

Indicators | CWS | Final Yield | Estimated Yield | |
---|---|---|---|---|

Morphology | $\mathrm{Culm}\mathrm{length}L$ | 0.800 (4) | 0.798 (4) | 0.873 (3) |

$\mathrm{Culm}\mathrm{wall}\mathrm{thickness}t$ | 0.871 (2) | 0.748 (6) | 0.772 (5) | |

$\mathrm{Leaf}\mathrm{area}{A}_{Leaf}$ | 0.660 (6) | 0.867 (1) | 0.821 (4) | |

$\mathrm{Leaf}\mathrm{angle}{\delta}_{Leaf}$ | 0.502 (8) | 0.431 (8) | 0.421 (8) | |

Physical properties | $\mathrm{Young}\u2019\mathrm{s}\mathrm{modulus}E$ | 0.879 (1) | 0.763 (5) | 0.747 (6) |

$\mathrm{Bending}\mathrm{energy}{W}_{m}$ | 0.591 (7) | 0.743 (7) | 0.660 (7) | |

$\mathrm{Culm}\mathrm{moisture}\mathrm{content}{w}_{c}$ | 0.856 (3) | 0.813 (3) | 0.841 (1) | |

$\mathrm{Leaf}\mathrm{moisture}\mathrm{content}{w}_{l}$ | 0.797 (5) | 0.818 (2) | 0.840 (2) |

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**MDPI and ACS Style**

Hu, X.; Li, H.; Wu, H.; Long, B.; Liu, Z.; Wei, X.; Li, J.
Modeling the Kinematic Response of Rice under Near-Ground Wind Fields Using the Finite Element Method. *Agronomy* **2023**, *13*, 1178.
https://doi.org/10.3390/agronomy13041178

**AMA Style**

Hu X, Li H, Wu H, Long B, Liu Z, Wei X, Li J.
Modeling the Kinematic Response of Rice under Near-Ground Wind Fields Using the Finite Element Method. *Agronomy*. 2023; 13(4):1178.
https://doi.org/10.3390/agronomy13041178

**Chicago/Turabian Style**

Hu, Xiaodan, Huifen Li, Han Wu, Bo Long, Zhijie Liu, Xu Wei, and Jiyu Li.
2023. "Modeling the Kinematic Response of Rice under Near-Ground Wind Fields Using the Finite Element Method" *Agronomy* 13, no. 4: 1178.
https://doi.org/10.3390/agronomy13041178