Analysis of Damage Characteristics and Fragmentation Simulation of Soybean Seeds Based on the Finite-Element Method

Abstract

Soybeans are a crucial crop, and it is therefore necessary to make accurate predictions of their mechanical properties during harvesting to optimize the design of threshing cylinders, minimize the breakage rate during threshing, and enhance the quality of the final product. However, a precise model for the mechanical response of soybean seeds under stress conditions is currently lacking. To establish an accurate finite-element model (FEM) for soybeans that can predict their mechanical behavior under various loading conditions, an ellipsoidal modeling approach tailored for soybeans is proposed. Soybeans harvested in Xinjiang were collected and processed as experimental materials; the average moisture content was 11.77%, there was an average density of 1.229 g/cm³, and the average geometric specifications (height, thickness, and width) were 8.50 mm, 7.92 mm, and 7.10 mm, respectively. Compression tests were conducted on the soybeans in vertical, horizontal, and lateral orientations at the same loading speed to analyze the load and damage stages of these soybeans harvested in Xinjiang. The experimental results indicate that as the contact area decreases, the crushing load increases, with soybeans in the horizontal orientation being able to withstand the highest ultimate pressure. When placed vertically, the soybeans are not crushed; in horizontal and lateral orientations, however, they exhibit varying degrees of breakage. The Hertz formula was simplified based on the geometric characteristics of soybeans, and the elastic moduli in the X, Y, and Z directions of the soybean seeds were calculated as 42.8821 MPa, 40.4342 MPa, and 48.7659 MPa, respectively, using this simplified Hertz formula. A model of the soybeans was created in SolidWorks Ver.2019 and imported into ANSYS WORKBENCH for simulation verification. The simulation results were consistent with the experimental findings. The research findings enhance the understanding of the mechanical behavior of soybean seeds and provide robust scientific support for the optimization of soybean processing technologies and the improvement of storage and transportation efficiency.

1. Introduction

As a key grain and oil crop, soybean occupies an important position in the global agricultural system, with its rich protein content and wide fields of application [1,2,3,4,5]. However, in China, the progress in the research and development of soybean harvesting machinery has not kept pace with the rapid expansion in the crop’s planting area. Due to the poor adaptability of rice–wheat combine harvesters with respect to soybeans, a high loss rate was generated in the process of soybean harvesting, [6,7,8]. It is particularly noteworthy that under the action of the threshing roller, the core component of the harvesting machinery, soybean seeds are easily damaged; this is one of the key factors causing the crushing of the soybeans [9,10]. The threshing roller plays an important role in separating the soybean kernel from the straw in the process of harvesting, but its high-speed rotation and strong friction often cause serious mechanical damage to the soybean kernel. These damages will not only reduce the overall quality grade of soybeans, but may also affect their market price, thus negatively affecting economic efficiency. More seriously, physical damage may also destroy the internal physiological structure of the soybean seeds, and then reduce the germination rate, which poses a potential threat to the crop’s subsequent planting effectiveness and crop yield. Therefore, exploring the causes of soybean crushing is of great significance for improving the parameters of threshing drums, improving the performance of soybean harvesting machinery, and ensuring the quality of the soybean crop.

The finite element method (FEM) is a numerical technique for solving partial differential equations (PDEs) and integral equations. It reduces an entire complex problem to a series of relatively simple problems in order to reach a solution by discretizing a continuous solution region into a finite number of interconnected subregions (i.e., finite elements) and applying an approximation function within each finite element. This method has a wide range of applications in engineering and science, especially in structural analysis, heat transfer, fluid dynamics, and so on. Published studies exploring the complex relationships between the damage conditions of various materials and the related mechanical properties and stress distributions make extensive use of mechanical testing and finite-element analysis techniques. Study [11] measured and analyzed the stress-distribution characteristics of soybean seeds with different moisture-content levels under pressure, observed the pressure crushing process, and obtained the characteristics of the pressure crushing. In Reference [12], the damage mechanisms of cassava seed collision damage was defined by finite-element analysis, and the seeding parameters optimal for reducing the damage were obtained, which provided a theoretical basis for the optimal design of planters. In Reference [13], the rheological model in the ABAQUS Ver.6.13 was used with finite-element analysis to successfully predict the mechanical behavior of biomass residue under compression and expansion, and the potential of this model in predicting the mechanical properties of biomass materials was verified. In Reference [14], the finite-element model was used to simulate the mechanical behavior of wood beams with joint defects in bending tests, and the accuracy of the model was verified by comparison with the experimental results. Aiming to determine the inaccuracy of models used to simulate the corn-crushing process, Study [15] established a finite-element model of corn seeds, analyzed the stress distributions under compression, obtained the micromechanical characteristics, provided parameters for optimizing the threshers, and verified the accuracy of the model by experiments. Study [16] used the finite-element method to simulate soybean collisions and analyze the stress and displacement changes during collision. It was found that the impact velocity and contact radius significantly affected the damage degree, and the influence law of seed volume on the maximum stress in-creased first and then decreased, and the displacement increased linearly.

Studying the crushing-related characteristics of soybeans has far-reaching significance for the environment; this is mainly reflected in the efficient use of resources, energy savings, emission reductions and prospects for sustainable development. First of all, by optimizing the soybean-crushing process, the material loss during processing can be reduced, the resource utilization rate can be improved, and the pressure on the environment can be reduced. At the same time, the by-products produced in the crushing process (such as soybean meal, soybean skin, etc.) can be further used as feed or biomass energy, reducing waste emissions and promoting the development of the circular economy. Second, studying the mechanical properties of soybeans can help to develop more efficient processing technologies and energy-saving equipment, thereby reducing energy consumption and greenhouse gas emissions, and thus combat climate change. In addition, optimizing the crushing process can reduce the generation of dust and wastewater, improve air and water quality, and reduce pollution in the environment. In the long term, improving the efficiency of soybean processing can reduce the demand for land and water resources, promote sustainable agricultural development, reduce ecosystem disturbance, and protect biodiversity. Finally, the research on the crushing-related characteristics of soybeans provides a scientific basis upon which the government can formulate environmental policies and standards, and helps to promote stricter environmental regulations and incentives which can be used to promote green production and the development of a low-carbon economy.

However, at present, most of the research on the damage-related mechanical properties of various materials are based on data utilizing a single loading direction for the whole simulation. Relatively speaking, there is a lack of comprehensive research on the determination of the mechanical properties of soybean in different directions, and the combined effects of these characteristics.

In this study, the mechanical behaviors and physical characteristics of Xinjiang soybean seeds under vertical compression, horizontal compression, and lateral com-pression were measured, and the crushing morphology of soybean was studied. Through the establishment of a finite-element model for the soybean, this study provides an effective means for predicting the mechanical behavior of soybean seeds under complex stress environments, and has important practical significance for improving the processing efficiency and quality of soybean seeds.

2. Materials and Methods

2.1. Test Material

A sample of soybean grains was collected from a local farm in the Xinjiang region of China during the soybean’s maturation period. Before any tests were performed, the collected soybean samples were screened to ensure that the selected soybean seeds were undamaged, free of pests, and of uniform color. Before testing, the sample was kept in a sealed plastic bag to prevent moisture changes or spoilage of soybean seeds due to outside forces.

2.2. Test Equipment

The equipment used for the test includes the TA.Xtplus texturizer produced by Stable Micro Systems, UK, the ZV-E10 series camera produced by SONY of Japan, electronic vernier calipers, an electric blast-drying oven produced by Germany LPKF laser electronics AG, a high-precision electronic scale produced by China Shanghai Sainyu Hengping Scien-tific Instrument Co., Ltd., high precision measuring cylinder produced by Shanghai Shenbo Glass Instrument Co., Ltd, and a high performance computer with Nvidia RTX4070S graphics card. These instruments are all purchased by Jiangsu University in China.

2.3. Testing Methods

2.3.1. Soybean Moisture-Content Test

Grain moisture content is an important parameter affecting grain strength [17,18,19,20,21,22]. The soybean seeds were divided into three groups, each with a grain mass of 50 g, and put into an electric blast-drying oven for the moisture-content test. The drying time was set at 24 h. After 24 h, the quality of the soybean seeds in the three groups was measured, and the soybean seeds were put into the drying oven again, as shown in Figure 1. Then, the grains were allowed to continue to dry, and the above operations were repeated until within each group, the quality did not change. The testing process is shown in the figure below. Where the initial mass of the grain in each group is marked as ${\mathrm{G}}_1$, and the grain mass after drying to the same quality is marked as ${\mathrm{G}}_2$, the soybean water content is determined as follows:

$$\mathrm{W}={\displaystyle \frac{{\mathrm{G}}_1-{\mathrm{G}}_2}{{\mathrm{G}}_1}}$$

(1)

2.3.2. Soybean Density Test

Seed density is another important parameter affecting seed strength [23,24,25]. Field soybeans were harvested at the maturity stage, and random samples of soybean seeds were taken back to the laboratory for quality measurement and volume measurement. When measuring the quality and volume of soybean grains, the corresponding parameters of 10, 20, 30, 40, and 50 grains were measured, respectively, as shown in Figure 2.

2.3.3. Soybean Geometric Parameter Test

In theoretical analyses, the geometric model of the soybean kernel is often described as ellipsoidal [26,27,28,29,30,31]. This description is based on the fact that the soybean kernel usually has an approximately elliptical cross-section and presents a certain proportional relationship in the three dimensions of length, width, and thickness. On the whole, it has a relatively uniform volume distribution and a smooth surface. This makes the ellipsoid a suitable geometric approximation model.

As shown in Figure 3, when measuring the height (i.e., the maximum length in the direction of the vertical axis X), thickness (perpendicular to the thickness of cross-section Y in the direction of height), and width (the maximum width in cross-section Z) of soybean grains, keep the caliper perpendicular to the contact surfaces of the soybean grains to ensure the accuracy of measurement results. Soybean grains harvested from fields in Xinjiang were selected as the research objects, and were randomly selected and divided into three groups, as shown in Figure 3.

2.3.4. Soybean Physical Properties Test

Before the finite-element analysis, it is necessary to know the elastic modulus of the grain [20,27,32,33,34,35,36]. The soybean grains with the above-measured geometric parameters were fixed on the texture analyzer TA.XTplus for a compression test, as shown in Figure 4. Under the same loading speed, three different compression methods were applied to soybean grains: vertical compression, flat compression, and side compression.

In the compression test of the soybean grains, the apparent contact elastic modulus of the soybean grains, as calculated by the Hertz formula, is as follows [37,38,39,40,41,42,43,44,45,46,47]:

$$\mathrm{E}={\displaystyle \frac{0.338\mathrm{F}(1-{\mathsf{\mu }}^2)}{{\mathrm{D}}^{3/2}}}{[{{\mathrm{K}}_{\mathrm{U}}\left({\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{U}}}}+{\displaystyle \frac{1}{{{\mathrm{R}}_{\mathrm{U}}}^{\prime }}}\right)}^{{\displaystyle \frac{1}{3}}}+{{\mathrm{K}}_{\mathrm{L}}\left({\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{L}}}}+{\displaystyle \frac{1}{{{\mathrm{R}}_{\mathrm{L}}}^{\prime }}}\right)}^{{\displaystyle \frac{2}{3}}}]}^{3/2}$$

(2)

In the formula, E is the apparent contact elastic modulus of the soybean kernel, the unit is MPa; F is the crushing load of the soybean kernel, the unit is N; D is the amount of deformation of the soybean kernel when it is broken, the unit is mm; μ is the Poisson’s ratio of the soybean, which is 0.4. ${\mathrm{R}}_{\mathrm{U}},{{\mathrm{R}}_{\mathrm{U}}}^{\prime }$ are the minimum and maximum curvature radii of the contact surface on the soybean kernel, in mm; ${\mathrm{R}}_{\mathrm{L}}$,${{\mathrm{R}}_{\mathrm{L}}}^{\prime }$ are the minimum and maximum curvature radii of the contact surfaces on the soybean kernel, in mm. ${\mathrm{K}}_{\mathrm{U}}$ and ${\mathrm{K}}_{\mathrm{L}}$ are constants determined by the radius of the principal curvature.

Since the curvature radius of the contact surface between the soybean kernel and the compression probe and the carrier plate is almost the same, the simplified Formula (2) is as follows:

$$\mathrm{E}={\displaystyle \frac{0.338\mathrm{F}(1-{\mathsf{\mu }}^2)}{{\mathrm{D}}^{3/2}}}{[{{2\mathrm{K}}_{\mathrm{U}}\left({\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{U}}}}+{\displaystyle \frac{1}{{{\mathrm{R}}_{\mathrm{U}}}^{\prime }}}\right)}^{{\displaystyle \frac{1}{3}}}]}^{3/2}$$

(3)

$${\mathrm{R}}_{\mathrm{U}}=[{\left({\displaystyle \frac{\mathrm{X}}{2}}\right)}^2+{\left({\displaystyle \frac{\mathrm{Y}}{2}}\right)}^2]$$

(4)

$${{\mathrm{R}}_{\mathrm{U}}}^{\prime }=[{\left({\displaystyle \frac{\mathrm{Z}}{2}}\right)}^2+{\left({\displaystyle \frac{\mathrm{Y}}{2}}\right)}^2]$$

(5)

$$\mathrm{c}\mathrm{o}\mathrm{s}\theta ={\displaystyle \frac{\frac{1}{{R_u}^{\prime }}-\frac{1}{Ru}}{\frac{1}{{R_u}^{\prime }}+\frac{1}{Ru}}}$$

(6)

From among the soybean grains harvested in the field, the samples were selected using the principle of random selection and divided into 3 groups; each group corresponds to a grain compression method. The elastic modulus E of each grain is obtained by substituting the experimental data into Formula (2).

2.4. Soybean Compression Test

Three kinds of compression tests were carried out on the soybean grains, at the same loading speed, using the texture analyzer TA.Xtplus: vertical compression, flat compression, and side compression tests. A diagram of these three compression modes is shown in Figure 5. In order to better understand the damage-related characteristics and the mechanism of the soybean grain during compression, the soybean grain samples that were broken under the three different compression methods were photographed. During the shooting process, a high-precision camera was used to capture the details of the damage, while ensuring that the photos clearly reflected the specific situation of the grain damage. Three typical examples were selected from the photos for detailed analysis in order to more comprehensively explore the damage mechanisms of soybean seeds during compression.

2.5. Soybean Finite-Element Model Establishment and Simulation

2.5.1. Simulation Platform

The ANSYS Workbench is ANSYS’s integrated engineering simulation platform, which provides a complete design-to-proof approach based on finite-element analysis technology. It integrates geometric modeling, mesh division, condition setting, solution, and post-processing to simplify processes and improve efficiency. The software features a friendly interface and powerful functionality, which is widely used in many industries. It helps engineers predict performance, optimize designs and reduce costs, and is an important tool for research and analysis [48,49,50,51].

2.5.2. Creation of the Soybean Kernel Material Properties in Workbench

There is no material attribute for the soybean kernel in the Workbench material library, so it is necessary to add soybean kernel material by means of the Engineering Data. The material properties of soybean grain are related to grain density; elastic moduli in the X, Y, and Z directions; Poisson’s ratio; and shear modulus. The Poisson’s ratio of soybean grains is 0.4, and the density of the soybean grains and the elastic moduli in three directions are determined according to the physical properties test described in the previous chapter. The shear modulus can be determined by using the Poisson’s ratio and the elastic modulus of the soybean grain; the relationships between the three parameters are shown in Equation (7).

$$\mathrm{G}={\displaystyle \frac{\mathrm{E}}{2(1+\mathsf{\mu })}}$$

(7)

2.5.3. Soybean Grain Shape Model Design

The soybean kernel consists of the seed umbilical, seed coat, and embryo. The mechanical properties of the soybean kernel are mainly affected by the seed coat. Therefore, a soybean kernel can be simplified into a solid and uniform linear elastic material. The shape of the soybean grain can be approximated to that of an ellipsoid.

A soybean kernel is composed of two cotyledons. In SolidWorks, a three-dimensional model of a cotyledon is first established, and then two cotyledons are combined to form a kernel model.

A round steel plate (base) is attached to the bottom of the soybean kernel to support the kernel, and a round steel plate (pressure block) is placed above the kernel to squeeze the kernel. The three-dimensional diagram is established in SolidWorks and saved in the *.x_t file format. The Geometry module in Workbench is opened, and the 3D soybean kernel map is imported into Workbench. The processed model is shown in Figure 6.

2.5.4. Simulation Settings

There are five contact modes in Workbench-mechanical, namely binding, no separation, no friction, rough and friction. In order to accurately simulate the actual working conditions, the contact mode between two grain blades is set as rough contact, which simulates the situation in which blades have a certain friction but are easy to slide. For the contact between the grain and the press block and between the grain and the base, the friction contact mode is adopted, and the friction coefficient is set at 0.32, a setting which can better reflect the interaction force between the materials. In view of the differences in structure and materials between the soybean grain, press block, and support base, this paper adopted specific strategies as to grid division. As for the core analysis object of the soybean kernel, its meshes are required to meet a high analysis accuracy level, so the surface meshes are selected and the mesh size is set at 0.5 mm to ensure the accuracy of the calculation results. In contrast, the grid division for the pressing block and the base relies on the system’s automatic partition function to achieve an efficient and reasonable grid layout, as shown in Figure 7. In the simulation process, the contact between the soybean kernel and the press block is regarded as a direct interaction between the surfaces. Given the different compression methods, the displacement of the compression block under vertical compression, flat compression, and side compression is set, respectively, as 4 mm, 3.55 mm, and 3.96 mm. At the same time, the support base is set as a fixed support, and the simulation time is set to 0.005 s to obtain the dynamic response data.

3. Results and Discussion

3.1. Soybean Kernel Physical Characteristics Test Results

3.1.1. Results of Soybean Grain Moisture-Content Test

Moisture content has a significant influence on the crushing-related characteristics of soybean in the threshing process. When the moisture content is too low, the beans are dry and brittle; although the mechanical strength is high, the brittleness is increased, and the soybean is easily broken under mechanical impact. When the moisture content is too high, the bean is soft, the mechanical strength is reduced, and the soybean is easily broken by extrusion or friction. In addition, the moisture content also affects the friction coefficient between the grain and the mechanical parts; too high a level will increase the friction, resulting in surface damage; too low a level may aggravate the breakage due to increased brittleness. Reasonable control of moisture content can maintain the elasticity and toughness of the grain in an optimal state, effectively disperse the mechanical impact force, and reduce the crushing rate.

After the soybean seeds were dried for 24 h, the quality of the soybean seeds in each group was recorded and the samples were then again put into the drying oven for drying. After two hours, the quality of the soybean seeds in each group was recorded; it was found that the quality was the same as that after 24 h of drying, indicating that soybean seeds had no water after 24 h of drying. The test results are shown in

Table 1. Test data of soybean grain moisture content.

Number of Tests	$\mathbf{Soybean} \mathbf{Kernel} \mathbf{Quality} \mathbf{Before} \mathbf{Test} {\mathbf{G}}_1$ [g]	$\mathbf{Soybean} \mathbf{Kernel} \mathbf{Quality} \mathbf{After} \mathbf{Test} {\mathbf{G}}_2$ [g]	$\mathbf{Soybean} \mathbf{Grain} \mathbf{Moisture} \mathbf{Content} \mathbf{W}$ [%]
1	50	44.07	11.86
2	50	44.15	11.70
3	50	44.12	11.76

, and indicate that there was little difference between the grain water content levels of the mature soybeans from Xinjiang. The average value of 11.77%, reflecting the three groups of experiments, was taken as the grain water content of Xinjiang soybeans during the harvest period.

3.1.2. Results of Soybean Kernel Density Test

The density of the soybean was calculated by analyzing the corresponding mass and volume of soybean grains, using different numbers of grains. The calculation and analysis processes are shown in

Table 2. Tests of soybean kernel density using different numbers of kernels.

Number of Soybean Grains [Grain]	Mass [g]	$\mathbf{Volume} [{\mathbf{c}\mathbf{m}}^3$]	$\mathbf{Density} [\mathbf{g}/{\mathbf{c}\mathbf{m}}^3]$
10	3.4495	2.9	1.189
10	3.4566	3.0	1.152
10	3.4454	2.8	1.231
20	6.5864	5.5	1.198
20	6.4987	5.4	1.203
20	6.6254	5.5	1.205
30	9.9368	8.1	1.227
30	9.8542	8.0	1.232
30	9.9556	8.1	1.229
40	13.1970	10.5	1.257
40	13.2564	10.6	1.251
40	13.6502	10.7	1.276
50	16.4090	13	1.262
50	16.5963	13.1	1.267
50	16.6554	13.2	1.262

. The average of the five groups of density test results in the table is taken as the soybean kernel density coefficient in this paper, and its value is 1.229 g/${\mathrm{c}\mathrm{m}}^3$.

3.1.3. Results of Soybean Grain Geometric Parameters Test

The height, thickness, and width of each grain were recorded with vernier calipers, and these measurement results are shown in

Table 3. Measurement results for the geometric parameters of the soybean kernel (vertical compression).

Test Number	Grain Height X [mm]	Grain Thickness Y [mm]	Grain Width Z [mm]
1	8.94	7.70	6.94
2	8.35	7.37	6.34
3	8.09	7.40	6.24
4	8.32	8.06	7.45
5	9.41	7.35	6.35
6	8.18	7.59	6.59
7	8.45	8.03	7.24
8	8.45	7.56	6.79
9	8.60	8.45	7.10

,

Table 4. Measurement results for soybean grain geometric parameters (flat compression).

Test Number	Grain Height X [mm]	Grain Thickness Y [mm]	Grain Width Z [mm]
1	8.19	8.22	7.29
2	8.91	8.10	7.04
3	7.71	8.08	7.35
4	7.93	7.94	7.19
5	8.89	8.42	7.92
6	8.95	8.33	7.50
7	8.68	8.24	7.27
8	8.53	7.85	7.41
9	8.58	8.05	7.15

and

Table 5. Measurement results for soybean grain geometric parameters (side compression).

Test Number	Grain Height X [mm]	Grain Thickness Z [mm]	Grain Width Y [mm]
1	8.29	7.68	6.98
2	8.05	7.73	7.15
3	8.83	8.08	7.35
4	8.68	8.24	7.27
5	8.53	7.85	7.41
6	8.58	8.05	7.15
7	8.24	8.02	7.50
8	8.39	7.63	6.73
9	8.76	7.89	7.09

. The soybean grain geometry parameters were determined as the average value of the three groups of soybean grain geometry size measurement data: height 8.50 mm, thickness 7.92 mm, and width 7.10 mm.

3.1.4. Results of Soybean Grain Compression Test

The soybean grains harvested in the field were selected by the principle of random selection and divided into three groups; each group corresponds to a grain compression method. Then, vertical compression, flat compression, and side compression tests were carried out, and these test results are shown in

Table 6. Results of soybean kernel compression test (vertical compression).

Test Number	Crushing Load F [N]	Modulus of Elasticity E [MPa]
1	135.038	27.4534
2	63.1661	28.6207
3	93.3991	29.3697
4	73.5115	27.9058
5	63.3912	42.3364
6	59.7021	93.3329
7	86.8667	60.7096
8	74.9535	53.2459
9	63.0531	57.9863

,

Table 7. Results of soybean grain compression test (flat compression).

Test Number	Crushing Load F [N]	Modulus of Elasticity E [MPa]
1	170.3092	28.1659
2	152.1623	34.0395
3	125.0894	39.7961
4	104.2491	48.3114
5	133.5587	80.5331
6	111.9748	70.6535
7	133.9003	54.3485
8	134.7555	63.1211
9	194.1357	31.0915

and

Table 8. Soybean kernel compression test results (side compression).

Test Number	Crushing Load F [N]	Modulus of Elasticity E [MPa]
1	63.1507	28.1801
2	125.0894	55.4765
3	91.4319	32.0896
4	113.2610	16.7267
5	88.7897	50.6841
6	90.5361	29.6400
7	67.5462	59.5812
8	61.4147	48.3532
9	93.4723	38.6106

. The elastic modulus E of each grain is obtained by substituting the experimental data into Formula (2).

As for the grain elastic moduli obtained under the three compression methods, the highest and lowest values were removed, and the average value obtained was taken as the grain elastic modulus in that direction. The elastic moduli of the soybean grains in the X, Y, and Z directions were 42.8821 MPa, 40.4342 MPa, and 48.7659 MPa, respectively. These values refer to the elastic modulus within the limit of linear deformation, i.e., the range in which the stress–strain relationship remains linear.

3.1.5. Soybean Material Setup in ANSYS

According to Formula (7), the shear moduli of the XY, YZ, and XZ planes are 1.5315 × 10⁷ Pa, 1.4441 × 10⁷ Pa, and 1.7416 × 10⁷ Pa, respectively. The properties of soybeans are shown in Figure 8.

According to the preliminary experimental research, the height, thickness, and width of soybean grain geometric model are 8.50 mm, 7.92 mm, and 7.10 mm, respectively.

A soybean kernel is composed of two cotyledons. In SolidWorks, a three-dimensional model of a cotyledon is first established, and then two cotyledons are combined to form a kernel model. The three-dimensional model of the soybean kernel is shown in Figure 9 and Figure 10.

3.2. Simulation Results

3.2.1. Vertical Compression

In the simulation of the vertical compression test, as shown in Figure 11, the simulation results showed that at 0.0026 s, the seeds began to be strongly squeezed by the compression block, resulting in the separation of their cotyledons. At this time, the minimum deformation on the grain was 0.0897 mm, indicating that even at the early stage of compression, the grain had already undergone a small deformation. The average deformation was 0.1041 mm, which showed the uniformity of the stress across the whole grain. At the same time, the maximum equal-effect force reached 0.13633 MPa, indicating that the grain was subjected to greater stress in the stressed region.

With the progress of the simulation, by 0.0105 s, the upper ends of the two leaves of the soybean kernel have been significantly separated, which indicates that the damage to the internal structure of the kernel has intensified. At this time, the minimum deformation increased to 0.0931 mm, while the average deformation increased sharply to 2.3145 mm, reflecting the significant deformation of the grain under continuous pressure. The maximum equivalent stress increased to 3.6851 MPa, indicating that the grain was seriously damaged under extreme stress conditions.

3.2.2. Flat Compression

In the simulation of horizontal compression test, the stress and deformation characteristics of the soybean kernel are different from those seen in the vertical compression. As shown in Figure 12, at 0.0263 s, the compacting block began to press down on the grain, resulting in an initial deformation of the two cotyledons. At this time, the maximum deformation was 0.5856 mm, the average deformation was 0.2762 mm, and the average equivalent stress on the grain was 0.26718 MPa. With continuous compression, the deformation of the two cotyledons became more obvious at 0.0368 s, and obvious fragmentation was observed in the upper and lower cotyledon. The maximum deformation increased to 0.8040 mm, the average deformation also increased, and the average equivalent stress reached 0.34209 MPa.

When the simulation time reached 0.0500 s, the fragmentation of soybean grains was very significant, and the edges of the two cotyledons were obviously separated. The maximum deformation was as high as 4.7745 mm, and the average deformation was 0.5135 mm. Although the amount of deformation continued to increase, the average equivalent stress decreased to 0.070891 MPa, which may be due to a failure of the internal structure of the grain which resulted in a change in the stress distribution. At 0.04 s, the equivalent stress on the grain reached its peak value, with an average value of 0.40737 MPa. Compared with vertical compression, there was no obvious cotyledon division in the soybean grains under horizontal compression; this was related to the flat structure of soybean grains.

3.2.3. Side Compression

In the simulation of the side compression test, as shown in Figure 13, at 0.0079 s, the compression block began to squeeze the grain, resulting in rapid separation of the two cotyledons, with the middle part already separated. At this time, the maximum deformation was 0.1670 mm, the average deformation was 0.0769 mm, and the average equivalent stress on the grain was 0.016297 MPa. With the deepening of compression, the splitting phenomenon of two cotyledons becomes more obvious at 0.0474 s, the average deformation increases to 0.9838 mm, and the average equivalent stress surges to 0.75667 MPa.

When the simulation time reached 0.0500 s, the damage of soybean kernel was further aggravated, and the two cotyledons of the soybean kernel showed obvious fragmentation-related phenomena, and the average deformation reached 1.0934 mm. Although the average equivalent stress decreased, it still maintained a high level of 0.53307 MPa. It was found that the equivalent stress on the grain reached its peak value at 0.0474 s, with an average value of 0.75667 MPa. The results showed that the stress and deformation of soybean grains under lateral compression were significantly different from those under vertical compression and lateral compression.

3.3. Compression Test Results

The test results are shown in Figure 14. Finally, the soybean grains obtained by the soybean harvester after the harvest operation were taken as a reference to show the soybean-crushing situation in the actual harvest.

Through the analysis described in Figure 14, the loading process of soybeans can be refined into the following four stages:

The first stage is the initial stage, from when soybean seeds are loaded until they break. At this stage, the texture analyzer makes initial contact with the soybean kernel, causing the pressure value to gradually change from zero. A relatively stable mechanical state is maintained between the soybean grain and the upper and lower pressure disc, and the load–displacement curve shows a linear increase. At this time, the soybean kernel mainly undergoes elastic deformation, and the pressure value increases with the increase of displacement. When the load on the soybean kernel suddenly decreases, the corresponding value of this point on the destruction–displacement curve is defined as the threshold value of the crushing load on the soybean kernel.

The second stage is the sudden-breaking stage of the soybean kernel. As shown in Figure 14a,c,e, when the loading force is suddenly reduced, the kernel will burst. At this stage, the separation of the cotyledons is mainly observed in the soybean grains placed vertically. In addition to the separation of the cotyledons, cotyledon fragmentation is also observed in the flat and side soybean grains.

The third stage is the unloading stage of the soybean kernel. When the force exerted on the soybean kernel reaches the critical value at which its structure is destroyed, the texture analyzer continues to compress the soybean kernel and further aggravate the damage. However, because the soybean kernel has been broken, its internal self-bonding strength is significantly reduced, so it enters the unloading state. With the continuous increase of displacement, the destructive force on soybean seeds began to decrease gradually.

The fourth stage is the permanent-deformation stage of the soybean kernel. At this stage, the soybean kernel is only subjected to the continuous pressure of the indentation machine, and no elastic deformation occurs. The pressure of the indentation machine causes significant deformation in the soybean kernel, and the destruction–displacement relationship shows nonlinear characteristics. With the continuous increase of displacement, the load may linearly decrease or increase until the soybean kernel is finally completely flattened.

A soybean kernel obtained after an actual harvest operation is shown in Figure 15. Broken soybean seeds are marked in black circles. The crushing-related characteristics of the soybean kernel obtained after an actual harvest operation are consistent with those of soybean kernel in the finite-element simulation, which proves the effectiveness of the finite-element model of the soybean kernel.

4. Conclusions

The material properties of soybean seeds and their damage-related characteristics under compression were studied by means of a texture analyzer and finite-element analysis, and the following experimental and simulation results were obtained:

(1) Based on the simplified Hertzian theoretical model for soybean grains and the relevant experimental data obtained from the compression tests using the texture apparatus, the elastic moduli of the soybean in the X, Y and Z directions were calculated as 42.8821 Mpa, 40.4342 MPa, and 48.7659 MPa, respectively. There is a significant correlation between the compression number for the soybeans and the rupture load, and this correlation is significantly affected by the placement method of the soybeans.

(2) The soybean kernel was analyzed for the full duration of the process, from loading to crushing. The period from the loading stage of soybean seeds to the crushing stage is divided into the elastic deformation stage, burst crushing stage, unloading stage, and permanent deformation stage. The separation of the cotyledons was the main load damage in soybean grain in the vertical state. In contrast, both cotyledon separation and cotyledon fragmentation occurred when the seeds were loaded horizontally or sideways. When observing the damage-related characteristics, it is obvious that the adhesion between the two cotyledons is relatively low.

(3) The model of Xinjiang soybean was established by using the ANSYS Ver.19.2 finite-element software, and the compression processes of soybean kernel under different placement methods were simulated and analyzed. The simulation results show a high consistency with the data obtained through the physical property test, which verifies the accuracy and reliability of the simulation analysis.