Research on the Construction of a Finite Element Model and Parameter Calibration for Industrial Hemp Stalks

Abstract

Finite element numerical simulations provide a visual and quantitative approach to studying the interaction between rigid mechanical components and flexible agricultural crops. This method is an important tool for the design of modern agricultural production equipment. Obtaining accurate material model parameters for crops is a prerequisite for ensuring the reliability and accuracy of numerical simulations. To address the issue of unclear mechanical constitutive model parameters for industrial hemp stalks, this study utilized the theory of composite materials to establish a mechanical constitutive relationship model for industrial hemp stalks. Compression, tensile, and bending tests on different components of the stalk were conducted, using a computer-controlled universal testing machine, to obtain their elastic parameters. Combined with the measured basic material parameters and contact parameters of industrial hemp stalks, a finite-element numerical simulation model of industrial hemp stalks was established. By conducting Plackett–Burman and central composite experiments, it was determined that among the six measured parameters, the anisotropic plane Poisson’s ratio of the phloem and the isotropic plane Poisson’s ratio of the xylem have a significant influence on the maximum bending force of the stalk. Parameter optimization was carried out, using the relative error of the maximum bending force as the optimization objective, resulting in an anisotropic plane Poisson’s ratio of 0.054 for the phloem and an isotropic plane Poisson’s ratio of 0.28 for the xylem of industrial hemp stalks. To validate the accuracy and reliability of the optimized parameters, a numerical simulation was conducted and compared with the physical experiments. The simulated value obtained was 405.81 N while the actual measured value was 392.55 N. The error between the simulated and measured values was only 3.4%, confirming the effectiveness of the model. The precise parameters for the mechanical characteristics of industrial hemp stalk material obtained in this study can provide a parameter basis for future research on the numerical simulation of mechanized industrial hemp harvesting and retting.

1. Introduction

Industrial hemp is a form of the cannabis plant with a tetrahydrocannabinol (THC) content below 0.3%, which does not possess any narcotic value [1,2]. Hemp has broad application prospects in fields such as textiles, papermaking, cosmetics, medicine, and composite materials [3,4,5,6,7]. In recent years, with the rapid development of industrial hemp production, many universities and research institutions have conducted extensive research into mechanized harvesting. Researchers have successfully furthered the development of machinery such as industrial hemp stalk harvesters, stalk and leaf harvesters, and stalk-leaf-seed harvesters [8,9,10,11,12]. Currently, the research methods used in the development of industrial hemp harvesting equipment mostly rely on traditional mechanism optimization design and experimental approaches; however, these methods have long development cycles and low efficiency and cannot meet the design requirements of modern agricultural machinery. With the advancement of technology and the promotion of agricultural modernization, numerical simulation techniques have begun to be applied in agricultural equipment design. Numerical simulation techniques, represented by the finite element method, are not limited by time or location. By constructing a numerical simulation model of agricultural machinery–crop systems, these techniques enable intuitive and quantitative research into the interaction between rigid mechanical components and flexible crop plants. They also offer advantages such as high efficiency, low cost, and shortened research and development cycles, making them an important tool for the design of modern agricultural production equipment [13,14,15].

To conduct numerical simulation research on the development of industrial hemp harvesting and stripping equipment, obtaining the accurate physical and mechanical properties of industrial hemp stalk materials is a prerequisite for ensuring the accuracy of numerical simulations. Recently, some researchers have conducted relevant studies on the mechanical properties of industrial hemp stalks [16,17,18]. However, these studies only involve partial mechanical property measurements of stalk materials, using specific instruments and under specific conditions. Due to the limitations of the experimental instruments and conditions, it is difficult to obtain the comprehensive and accurate parameters that are required for constructing a numerical model for industrial hemp stalks. Regarding parameters that cannot be measured directly, approximate values are often used, resulting in the compromised accuracy of the model.

In solving the problem of unclear numerical model parameters, parameter calibration is commonly used. Relevant research includes: Shi et al. [19] studied the lack of stalk models and contact parameters via numerical simulation research into the key steps in sesame harvesting, such as stalk posture changes. They focused on sesame stalks as the research object, constructed a flexible numerical model of sesame stalks using the discrete element method, and calibrated the intrinsic parameters and contact parameters of different parts of the sesame stalk by employing experimental values at different levels. Through these parameter calibration experiments, they determined the contact parameters between sesame stalks, and between the stalks and harvesting equipment, and verified the correctness of the model through experimental development. Similarly, Wang et al. [20] addressed the lack of accurate finite element numerical simulation models for the mechanical harvesting of wild chrysanthemums. They focused on the stalks of wild chrysanthemums during the harvesting period. Using the ANSYS Workbench and LS-DYNA software (17.2 version) programs, they established a numerical simulation model for the cutting of chrysanthemum stalks, based on a plastic–kinematic failure model. By conducting parameter calibration, they obtained precise parameters for the most significant factors affecting the maximum cutting force. In order to improve the accuracy of the parameters (such as the alfalfa straw–alfalfa straw static friction coefficient, the alfalfa straw–alfalfa straw rolling friction coefficient, the shear modulus of alfalfa straw, Poisson’s ratio of alfalfa straw, alfalfa straw–alfalfa straw restitution coefficient, etc.) used in discrete element simulation studies during the compression of alfalfa straw, Ma et al. [21] conducted Plackett–Burman experiments to screen for significant factors, and Box–Behnken experiments to establish a regression equation model between the stacking angle of alfalfa straw and three of the factors (alfalfa straw–alfalfa straw static friction coefficient, alfalfa straw–alfalfa straw rolling friction coefficient, and alfalfa straw–45 steel static friction coefficient). They obtained precise values for the dynamic and static friction coefficients of alfalfa straw against alfalfa straw, as well as the static friction coefficient between alfalfa straw and 45 steel, then validated the accuracy of the model. The above research demonstrates that parameter calibration provides an effective method for addressing the issue of inaccurate parameters in numerical simulation models.

Against this background, the present study will conduct an experimental determination of the basic mechanical properties of stalk materials and analyze the parameters of the constitutive models. On this basis, the parameter range for the optimization experiments will be determined. Subsequently, Plackett–Burman experiments and central composite numerical simulation experiments will be conducted using finite element techniques to calibrate the engineering constants of industrial hemp stalk materials. Finally, numerical simulations and physical experimental comparative tests will be conducted to verify the accuracy of the finite element numerical simulation model, focusing on the prevalent deformation mode for stalk bending deformation during mechanized harvesting and the fiber-stripping processes of industrial hemp. The precise mechanical property parameters of industrial hemp stalk materials obtained through this study can provide parameter foundations for further numerical simulations.

2. Experimental Analysis of the Mechanical Properties of Industrial Hemp Stalks

2.1. Constitutive Relationship of Industrial Hemp Stalk Material

The geometric structure of industrial hemp stalk material is illustrated in Figure 1, comprising an approximately cylindrical composition of phloem, xylem, and medulla space. Apart from the medulla, the industrial hemp stalk, which is composed of phloem and xylem tissues, exhibits transversely orthotropic material properties [22,23]. The engineering elastic parameters of the material satisfy the following equation:

$$\{\begin{array}{l}{E}_X=E_Y\\ G_{YZ}=G_{XZ}\\ {\mu }_{YZ}={\mu }_{XZ}\\ G_{XY}=\frac{E_X}{2(1+{\mu }_{XY})}\end{array}$$

(1)

where E_X and E_Y are the radial elastic moduli, and E_Z is the axial elastic modulus; G_XY represents the in-plane shear modulus for isotropic materials, while G_YZ and G_XZ represent the in-plane shear moduli for anisotropic materials. µ_XY represents the in-plane Poisson’s ratio for isotropic materials, while µ_YZ and µ_XZ represent the Poisson’s ratios for anisotropic materials.

2.2. Mechanical Testing of Industrial Hemp Stalks

The test materials were acquired from the “Wan Da Ma 1” variety of industrial hemp plants grown at the Agricultural Science Academy of Lu’an City, Anhui Province, China. This variety was successfully bred by the Agricultural Science Academy of Lu’an City, Anhui Province in 2007. Currently, it is the main cultivated variety in the local area and possesses regional representativeness. The selected materials were sourced from fresh industrial hemp plants with good growth, free from pests and diseases, and with straight stalks. During the harvesting of industrial hemp using a harvester, the threshing device and gripping conveyor primarily come into contact with the hemp stalks at a position 45 cm above the root. Therefore, samples were randomly selected from the stalks at a position 45 cm above the root for testing purposes. The SUNS-UTM6503 microcomputer-controlled electronic universal testing machine was used for testing, with a standard load capacity of 5 kN and a sensor accuracy of 0.1%. The mechanical property parameters were measured through radial compression, axial tension, and radial bending tests, as shown in Figure 2.

By conducting radial compression tests on the test samples, the radial elastic moduli, E_X and E_Y, of each component of the stalk can be obtained. Similarly, conducting axial tension tests on the samples provides the axial elastic modulus E_Z of each component of the stalk [24].

By performing three-point bending tests on the samples and using Equations (2) and (3), the anisotropic out-of-plane shear modulus G_XZ of the xylem and of the whole stalk can be determined:

$$U=\frac{\Delta p·L}{4(f-\frac{f_1·L}{3a})}$$

(2)

$$G=\frac{2U}{\pi /4(D^2-d^2)}=2.564\frac{U}{D^2-d^2}$$

(3)

where U is the shear stiffness, N; Δp is the incremental load in the elastic phase, N; L is the span in mm; f is the incremental mid-span deflection in mm; f₁ is the incremental deflection at the free end in mm; a is the free end extension length in mm. G is the shear modulus, in MPa; D is the outer diameter of the specimen in mm; d is the inner diameter of the specimen in mm.

Due to the soft texture of the phloem, it is not feasible to conduct three-point bending tests. The anisotropic planar radial shear modulus, G_XZ, of the phloem can be calculated using Equations (4) and (5):

$$\{\begin{array}{l}{V}_M=\frac{{\left(D-2h\right)}^2-d^2}{D^2-d^2}\\ V_R=1-V_M\end{array}$$

(4)

$$G_{XZ}=\frac{V_M\times G_{XZ}\times G_{XZ}}{G_{XZ}-V_R\times G_{XZ}}$$

(5)

where V_M is the volume fraction of the xylem in the stalk; V_R is the volume fraction of the phloem in the stalk; h is the thickness of the phloem component in mm.

Due to the limitations of the mechanical testing equipment, it is not possible to directly determine the Poisson’s ratio. Referring to the existing literature [25,26], the initial values for the isotropic plane Poisson’s ratio, µ_XY, are set to 0.3 for both the phloem and xylem. Since there is a relationship between the parameters of the anisotropic materials, as described by Equation (6), the anisotropic plane Poisson’s ratio can be calculated using this formula. Specifically, for the phloem, the anisotropic plane Poisson’s ratio, µ_XZ = µ_YZ < 0.076, is assigned an initial value of 0.05. For the xylem, the anisotropic plane Poisson’s ratio, µ_XZ = µ_YZ < 0.483, is assigned an initial value of 0.3.

$${\mu }_{YZ}<\frac{1}{\sqrt{2{\mu }_{YZ}}}\times \frac{E_X}{E_Z}$$

(6)

2.3. Experimental Results

By conducting radial compression tests, axial tensile tests, and radial bending tests, along with theoretical calculations, the engineering constant parameters of the various components of the hemp stalk can be obtained, as shown in

Table 1. The engineering constant parameters of each part of the hemp stalk.

	Parameters	EX (MPa)	EY (MPa)	EZ (MPa)	GXY (MPa)	GXZ (MPa)	GYZ (MPa)	µXY	µXZ	µYZ
Part
Phloem		58.99	58.99	2000.78	22.69	43.90	43.90	0.3	<0.076	<0.076
Xylem		34.73	34.73	73.22	13.36	49.83	49.83	0.3	<0.483	<0.483

.

3. Finite Element Model Construction

3.1. Basic Material Parameter Determination

Sixty industrial hemp stalk specimens were randomly selected for the study. The diameters of the specimens were measured using a Vernier caliper. Measurements were taken at the two ends and in the middle position of each specimen, and the average of three measurements was taken as the stalk diameter value. Through measurements and calculations, the average outer diameter of the stalk was determined to be 18.65 mm, while the inner diameter was 5.64 mm, and the phloem thickness was 0.85 mm. The volume ratios of the xylem and phloem in the stalk were found to be 0.843 and 0.157, respectively. The distribution curve of the obtained measurements is shown in Figure 3.

3.2. Stalk Contact Parameter Determination

The process of the mechanized harvesting and processing of industrial hemp involves contact between the metal mechanical components and the biological hemp stalk. The coefficient of friction between the hemp stalk and the metal components could be an important factor affecting the quality of operations. Therefore, it is necessary to determine the friction coefficient between the two. The determination of the friction coefficient in this study was performed using the incline plane method [27,28]. The friction test system constructed based on this method mainly consisted of a American Fastec HiSpec5 high-speed camera, a universal testing machine, a digital display angle sensor, control software, an inclined plane, and a photographic lamp, as shown in Figure 4. The Fastec HiSpec5 high-speed camera’s technical parameters are shown in

Table 2. Technical parameters of the Fastec Hispec 5 high-speed camera.

Technical Parameters	Value
Pixels	1696 × 1710
Maximum Shooting Speed	298,851 Frames/s
Pixel Size	8 × 8 μm
Sensitivity	1600 ISO Black and White 1000 ISO Color
ISO Range	19.27 mm
Shutter Speed	2 μs−1 s
Spectral Bandwidth	400–900 nm
Operating Environment	+5–35 °C

, while the UTM6503 computer-controlled universal testing machine’s technical parameters are shown in

Table 3. Technical parameters of UTM6503 computer-controlled universal testing machine.

Technical Parameters	Value
Maximum Test Force	5 kN
Accuracy Grade	0.5
Measurement Range	0.4~100% FS
Displacement Resolution	0.04 μm
Stress Control Rate Range	0.005~5% FS/s
Strain Control Rate Range	0.005~5% FS/s
Displacement Control Rate Range	0.001~500 mm/min

. During the experiment, the angle of the inclined plane was adjusted by slowly raising one end of the inclined plane using the universal testing machine. A high-speed camera was used to capture real-time images of the movement of the hemp stalk, and the collected images were subsequently processed using the Proanalyst Post-Processing software to obtain the relevant data on friction parameters. At the same time, in order to improve the shooting effect, a blue plate was used as the camera background the shooting frame rate was set to 400 fps, and the exposure time was 1438 µs, according to the experimental requirements.

The determination of the static friction coefficient is based on the following method and principles: hemp stalk samples, prepared in a rectangular shape, with dimensions of 10 mm in length and 5 mm in width, were placed on the inclined plate. The incline angle of the plate was gradually increased by pulling on it with the universal testing machine, then the reading on the digital display angle sensor was observed, using the high-speed camera, at the point when the sample first started to slide on the inclined surface. At this point, the incline angle of the plate was equal to the static friction angle of the object on the incline. The experimental principle is shown in Figure 5.

By eliminating m and g from the equations, where f_s = μ_sF_n = mgsinθ₁ and F_n = mgcosθ₁, the following equation can be obtained:

$${\mu }_{\mathrm{s}}=\tan {\theta }_1.$$

(7)

In Equation (7), f_s represents static friction force, N; F_n represents the normal force, N; m represents the mass of the sample in kg; g represents gravitational acceleration in m/s²; μ_s represents the coefficient of static friction; θ₁ represents the angle between the inclined plane and the horizontal plane.

The method for determining the coefficient of sliding friction and its experimental principle is as follows. Prepared samples of industrial hemp stalks are allowed to slide down an inclined plane with a certain slope. Based on the data concerning the incline angle, sliding length, and sliding time, the coefficient of sliding friction can be calculated using the corresponding formulas. The experimental principle is illustrated in Figure 6.

By eliminating g from the equations x = at²/2 and a = gsinθ₂ − μ_dgcosθ₂, the following equation can be obtained:

$${\mu }_{\mathrm{d}}=\tan {\theta }_2-\frac{2x}{g{t}^2\cos {\theta }_2}$$

(8)

In this equation, μ_d represents the sliding friction coefficient; x represents the sliding length in m; g represents gravitational acceleration in m/s²; t represents the falling time in s; and θ₂ represents the angle between the inclined plane and the horizontal plane.

Figure 7 shows the sliding photograph of the industrial hemp stalk samples on the contact surface of a steel plate, taken with a high-speed camera during the measurement of the sliding friction coefficient. Since the frame rate of the high-speed camera used in the experiment is 400 frames per second (fps), the time interval between two frames is 0.0025 s. By calculating the number of frames, the sliding time of the sample can be obtained. The sliding length can be measured using either a ruler or scale paper. The angle between the steel plate and the horizontal plane is measured using a digital display angle sensor. With the use of Equation (8), the sliding friction coefficient of the industrial hemp stalk sample can be calculated.

After randomly selecting 15 sets of different industrial hemp stalk samples, the static friction coefficient and sliding friction coefficient were measured. The experimental results were statistically analyzed, yielding an average static friction coefficient between the industrial hemp stalk and the steel plate of 0.55, with a maximum value of 0.65 and a minimum value of 0.42. The average sliding friction coefficient between the industrial hemp stalk and the steel plate was found to be 0.28, with a maximum value of 0.35 and a minimum value of 0.19.

3.3. Finite Element Model Parameter Determination

Based on the fundamental parameters of the stalk material, as determined in Section 2.1, a three-dimensional model of the industrial hemp stalk bending process was created using Creo software. The model was then converted to an STP file and imported into the Workbench LS-DYNA module. In the Workbench LS-DYNA module, the base, pressure head, supporting bases, and stalk were meshed. The mesh size for the industrial hemp stalk was set to 2 mm, resulting in a total of 12,620 elements. The finite element bending model of the industrial hemp stalk is shown in Figure 8.

According to the material properties defined in the Engineering Data module, the xylem and phloem regions of the industrial hemp stalk were modeled using orthotropic elastic materials. The material used for both the supporting bases and the plunger was structural steel. The engineering constants of each component of the stalk, as obtained in Section 2.3, were defined as the material properties of the hemp stalk in the Engineering Data module. The material parameters are shown in

Table 4. Material parameters of industrial hemp stalk in the engineering data module.

	Paramters	Density (kg/m3)	EX (MPa)	EY (MPa)	EZ (MPa)	GXY (MPa)	GXZ (MPa)	GYZ (MPa)	µXY	µXZ	µYZ
Part
Phloem		950	58.99	58.99	2000.78	22.69	43.90	43.90	0.3	0.05	0.05
Xylem		950	34.73	34.73	73.22	13.36	49.83	49.83	0.3	0.3	0.3

.

In order to reduce computation time before bending, the distances between the contact surfaces should be kept as close as possible. Based on the previously determined dynamic and static friction coefficients, the static friction coefficient between the industrial hemp stalk and the base/pressure head was set to 0.55, and the dynamic friction coefficient was set to 0.28. Boundary conditions were applied to the model, with the base fixed, the pressure head constrained in the X and Y directions for displacement and constrained in the X, Y, and Z directions for rotation. The industrial hemp stalk was unconstrained. The loading direction for the pressure head was set to the Z direction, with a loading rate of 100 mm/min. At this speed, the loading time was 12 s until the stalk was completely broken; therefore, the loading time was set to 12 s. Since Workbench 19.2 cannot directly output the contact forces, the d3plot file was opened and read using the LS-PrePost-4.5-x64 software. The bending diagram of the stalk is shown in Figure 9.

4. Parameter Calibration

4.1. Plackett–Burman Experiment

The Plackett–Burman experiment was conducted using the Design-Expert 8.0.6 software to compare the differences between the high and low levels of the experimental factors and the overall differences [29,30]. The aim was to identify those factors that significantly affect the maximum bending force, Q. The Plackett–Burman experiment considered the following factors: phloem density, xylem density, Poisson’s ratio in the isotropic plane of the phloem, Poisson’s ratio in the anisotropic plane of the phloem, Poisson’s ratio in the isotropic plane of the xylem, Poisson’s ratio in the anisotropic plane of the xylem, the static friction coefficient between the stalk and the steel plate, and the sliding friction coefficient between the stalk and the steel plate. The experimental parameter design is presented in

Table 5. Plackett–Burman test parameters.

Factors	Coding	Low Level	High Level
Poisson’s ratio in the isotropic plane of phloem	X1	0.2	0.4
Poisson’s ratio in the anisotropic plane of phloem	X2	0.03	0.07
Poisson’s ratio in the isotropic plane of xylem	X3	0.2	0.4
Poisson’s ratio in the anisotropic plane of xylem	X4	0.2	0.4
Static friction coefficient between the stalk and the steel plate	X5	0.42	0.65
Sliding friction coefficient between the stalk and the steel plate	X6	0.19	0.35

, with each parameter having two levels of high and low.

A Plackett–Burman experimental design where N = 12 was selected [31,32], as shown in

Table 6. The Plackett–Burman experimental design and results.

Experiment No.	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	Max. Bending Force F/N
1	−1	1	1	−1	1	1	1	−1	−1	−1	1	320.50
2	1	1	−1	−1	−1	1	−1	1	1	−1	1	353.83
3	1	−1	−1	−1	1	−1	1	1	−1	1	1	350.80
4	−1	−1	−1	1	−1	1	1	−1	1	1	1	357.94
5	−1	1	1	1	−1	−1	−1	1	−1	1	1	324.76
6	−1	1	−1	1	1	−1	1	1	1	−1	−1	351.06
7	1	1	1	−1	−1	−1	1	−1	1	1	−1	309.99
8	1	−1	1	1	−1	1	1	1	−1	−1	−1	334.84
9	1	1	−1	1	1	1	−1	−1	−1	1	−1	339.58
10	1	−1	1	1	1	−1	−1	−1	1	−1	1	326.07
11	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	357.71
12	−1	−1	1	−1	1	1	−1	1	1	1	−1	330.81

. Parameters X₁ to X₆ were set at the levels given in Table 5, while X₇ to X₁₁ were left blank for error analysis. The experimental results are presented in the last column of Table 6.

Based on the Plackett–Burman experimental results presented in Table 6, a significance analysis of the regression model for maximum bending force was conducted. The results are shown in

Table 7. Analysis of the significance of the parameters in the Plackett–Burman experiment.

Parameter	Standardization Effect	Sum of Squares	Contribution Rate/%	F	P
Model		2656.42		11.84	0.0079
X1	−46.12	63.80	2.24	1.71	0.2483
X2	−97.42	284.70	10.01	7.61	0.0399 *
X3	−273.25	2239.97	78.78	59.90	0.0006 **
X4	17.68	9.38	0.33	0.25	0.6377
X5	−33.75	34.17	1.20	0.91	0.3830
X6	28.52	24.40	0.86	0.65	0.4560

Note: * represents a significant value (p < 0.05), ** represents a highly significant value (p < 0.01).

, and the regression model for Q was obtained, as follows:

$$Q=398.63-23.06X_1-243.54X_2-136.63X_3+8.84X_4-14.67X_5+17.82X_6$$

(9)

Based on Table 7, the P-value of the model is 0.0079 < 0.01, and the R₂ is 0.9342, indicating that the main effects model is significant and that the fitted regression equation agrees well with the actual situation, which can be used to represent the influence of factors X₁ to X₆ on the response variable of maximum bending force. According to the significance level, the effect of the xylem’s isotropic plane Poisson’s ratio on the maximum bending force of the stalk is extremely significant, while the effect of the phloem’s anisotropic plane Poisson’s ratio is significant, and the effects of other factors are not significant. Combined with the contribution rate of significance analysis, X₃ has the greatest impact on the response value, with a contribution rate of 78.78%, followed by X₂, with a contribution rate of 10.01%, while the contribution rates of other factors are relatively small.

To select the factors X₂ and X₃, which have a significant influence on and contribution to the maximum bending force of the stalk, a steepest ascent experiment and a central composite experiment were conducted. For factors X₂ and X₃, their levels were increased according to the standardized effect values. The target value for the maximum bending force was set to the average value of five three-point stalk-bending tests, which is 339.76 N, while the levels of the remaining factors were set to their average values. The relative error between the maximum bending force, Q, obtained from the steepest ascent experiment and the maximum bending force, T, obtained from the actual three-point bending test was used to determine the level values for the optimal solution in the central composite experiment. The calculation formula is as follows:

$$\eta =\frac{\left|Q-T\right|}{T}\times 100\%.$$

(10)

According to

Table 8. Test scheme and results of the steepest ascent experiment.

Serial Number	X2	X3	Max. Bending Force for Steepest Ascent Experiment Q/N	Relative Error η /%
1	0.03	0.4	331.38	2.47
2	0.038	0.36	332.91	2.02
3	0.046	0.32	336.82	0.87
4	0.054	0.28	340.44	0.20
5	0.062	0.24	344.47	1.39
6	0.07	0.2	347.50	2.28

, as the value of X₂ gradually increases and X₃ decreases, the maximum bending force of the industrial hemp stalk increases. The relative error initially decreases and then increases. The minimum relative error is observed in the fourth experiment. To accurately determine the mechanical property parameters of the industrial hemp stalk, a central composite experiment was conducted using the parameters from the fourth experiment in the steepest ascent experiment as the central values. The parameters from the third and fifth experiments were used as the −1 level and +1 level, respectively. The maximum bending force of the stalk was considered as the response variable to seek the optimal solution.

4.2. Central Composite Experiment

Based on the results of the steepest ascent experiment, a central composite experiment was conducted to investigate the effects of the anisotropic Poisson’s ratio of the phloem (X₂) and the isotropic Poisson’s ratio of the xylem (X₃) on the maximum bending force (S) of the industrial hemp stalk. In this simulation experiment, the other parameters were set according to the parameters of the steepest ascent experiment. The experimental design scheme and results are shown in

Table 9. Central composite experiment factors and coding.

Codes	Factors
	Poisson’s Ratio in the Anisotropic Plane of Phloem	Poisson’s Ratio in the Isotropic Plane of Xylem
−1.414	0.043	0.22
−1	0.046	0.24
0	0.054	0.28
1	0.062	0.32
1.414	0.065	0.34

and

Table 10. Experiment design scheme and results of the central composite experiment.

Experiment Number	X2	X3	Max. Bending Force S/N	Relative Error η/%
1	0	0	340.44	0.002
2	1.414	0	338.70	0.003
3	1	1	344.47	0.014
4	0	0	340.44	0.002
5	0	1.414	342.40	0.008
6	1	1	335.77	0.012
7	−1	1	335.74	0012
8	0	0	340.44	0.002
9	−1.414	0	335.73	0.012
10	−1	−1	336.82	0.009
11	0	0	340.44	0.002
12	0	−1.414	331.01	0.026
13	0	0	340.44	0.002

, respectively.

The regression model equation for the maximum bending force, S, can be obtained by performing quadratic regression analysis on the test results given in Table 10, as follows:

$$S=340.44+1.49X_2-2.97X_3-2.45X_2{X}_3-1.30X_2^2-1.56X_3^2.$$

(11)

According to

Table 11. Significance analysis of response surface optimization experiment.

Source of Variation	Sum of Squares	df	F	P-Value
Model	137.36	5	14.15	0.0015 **
X2	17.64	1	9.08	0.0196 *
X3	70.38	1	36.24	0.0005 **
X2X3	23.91	1	12.31	0.0099 **
$X_2^2$	11.80	1	6.08	0.0431 *
$X_3^2$	16.88	1	8.69	0.0215 *
Residual	13.59	7
Lack of Fit	13.59	3
Error		4
Cor Total	150.95	12

Note: * represents a significant value (P < 0.05), ** represents a highly significant value (P < 0.01).

, the quadratic regression model for the maximum bending force showed a significance level of p ≤ 0.01 and a coefficient of determination of R₂ = 0.9099. This indicates that the regression model was statistically significant and adequately fitted the data, accurately reflecting the relationship between S and X₂, X₃, and their interactions. Among the factors, X₃, X₂X₃ were highly significant, while X₂, $X_2^2$, and $X_3^2$ were significant. There was a quadratic non-linear relationship between the experimental factors X₂, X₃, and the maximum bending force, S, and the interaction effect significantly impacted the maximum bending force. The response surface plot of the maximum bending force is shown in Figure 10.

Based on the results of the central composite experiment and the quadratic regression equation, the objective was to minimize the relative error of the maximum bending force of the industrial hemp stalk, taking into account factors X₂ and X₃. The objective function and constraint conditions were set as follows:

$$\{\begin{array}{l}\min \eta (X_2,X_3)\\ s.t.\{\begin{array}{l}-1.414\le X_2\le 1.414\\ -1.414\le X_3\le 1.414\end{array}\end{array}.$$

(12)

Through optimization, the final values for the industrial hemp stalk’s anisotropic plane Poisson’s ratio of the phloem and isotropic plane Poisson’s ratio of the xylem were determined to be 0.054 and 0.28, respectively.

4.3. Experimental Validation

To ensure the feasibility, accuracy, and universality of the model parameters, it is necessary to validate the experimental results. The validation experiment adopted a combined approach, with a simulation experiment and a physical experiment. The physical experimental method involved randomly selecting an industrial hemp stalk located 45 cm above the ground. The outer diameter of the phloem was measured to be 19.05 mm, and the thickness was 0.71 mm. The outer diameter of the xylem was 17.63 mm, and the thickness was 6.42 mm. The three-point bending test was conducted on a universal testing machine with a loading speed of 100 mm/min. The maximum bending force of the industrial hemp stalk could be obtained through the experiment. The bending test of the stalk is shown in Figure 11. Here, A represents the magnified view of the ruler’s scale.

The numerical simulation method involved creating a three-dimensional model of the industrial hemp stalk using Creo PTC software and defining the materials and constraints with the Workbench software. A vertical downward motion speed of 100 mm/min was set for the simulation experiment. A comparison was made between the maximum bending force curve, obtained from the three-point bending test on the universal testing machine, and the simulated bending force curve, obtained from the numerical simulation experiment. The results are shown in Figure 12.

From Figure 12, it can be observed that the maximum bending force of the industrial hemp stalk in the finite element model is 405.81 N in the simulation experiment, while in the measurement experiment on the universal testing machine, the maximum bending force is 392.55 N. The error between the simulated value and the actual measured value is 3.4%. This indicates that the simulated experimental results are consistent with the actual measured results, validating the reliability and accuracy of the finite element simulation model for industrial hemp stalk material.

Comparing the findings with those in similar research in the literature, it was found that the results obtained from the parameter calibration of industrial hemp stalks in this study are inconsistent with those in the literature [23]. This is due to the significant differences in the physical and mechanical properties of the internal structural components between industrial hemp and ramie, although they are both fiber crops.

5. Conclusions

(1)

Based on the constitutive nature of industrial hemp stalk material, which exhibits transverse orthotropic properties, radial compression, axial tension, and radial bending tests were conducted on the phloem and xylem components of industrial hemp stalks. Combined with an analysis using composite material theory, the engineering constant parameters of each component of industrial hemp stalks were determined.

(2)

By employing an inclined plane instrument, angle sensors, and a high-speed camera, physical experiments were conducted to determine the average static friction coefficient between industrial hemp stalks and steel plates, which was found to be 0.55, with a maximum value of 0.65 and a minimum value of 0.42. The average dynamic friction coefficient between the industrial hemp stalks and steel plates was found to be 0.28, with a maximum value of 0.35 and a minimum value of 0.19.

(3)

A numerical simulation model for the bending of industrial hemp stalks was constructed. By conducting Plackett–Burman experiments, the most significant factors affecting the maximum bending force on the stalks were identified as the anisotropic plane Poisson’s ratio of the phloem and the isotropic plane Poisson’s ratio of the xylem component. The static and dynamic friction coefficients between the stalk and the steel plate have no significant effect on the maximum bending force of the stalk. Through central composite experiments, parameter optimization was performed using the relative error of the maximum bending force as the optimization objective. The optimized values for the anisotropic plane Poisson’s ratio of the phloem and the isotropic plane Poisson’s ratio of the xylem component were found to be 0.054 and 0.28, respectively. At these optimized parameter values, the simulated bending force was 405.81 N, while the actual measured value was 392.55 N, resulting in an error of 3.4% between the simulated and measured values.

In this paper, a physical bend test was used as a comparison to calibrate the numerical simulation’s model parameters of the stalks of industrial hemp, which filled the research gap on the finite element bending model parameters of industrial hemp stalk.