Parameter calibration of a discrete element model for a mixture of cotton stalks and residual film

Parameter calibration of a discrete element model for a mixture of cotton stalks and residual film

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Jinming Li, Jiaxi Zhang^*, Yichao Wang, Jiangtong Yu, Chunxiao Xing

International Journal of Agricultural and Biological Engineering | 2026, 19(3) : 80 - 88

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International Journal of Agricultural and Biological Engineering | 2026, 19(3): 80-88

• Applied Science, Engineering and Technology (ASET) •

Parameter calibration of a discrete element model for a mixture of cotton stalks and residual film

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Jinming Li, Jiaxi Zhang^*, Yichao Wang, Jiangtong Yu, Chunxiao Xing

Affiliations

College of Mechanical and Electrical Engineering, Xinjiang Agricultural University, Urumqi 830052, China

Jinming Li, PhD candidate, research interest: recycling agriculture technology and equipment, Email: xjaujinmingli@163.com

Yichao Wang, PhD, research interest: harvesting machinery, Email: 360318122@qq.com

Jiangtong Yu, PhD, research interest: recycling of agricultural technology and equipment, Email: yujtong@163.com

Chunxiao Xing, PhD, research interest: recycling agriculture technology and equipment, Email: xcx@xjau.edu.cn

About Author:

Jinming Li, PhD candidate, research interest: recycling agriculture technology and equipment, Email: xjaujinmingli@163.com

Yichao Wang, PhD, research interest: harvesting machinery, Email: 360318122@qq.com

Jiangtong Yu, PhD, research interest: recycling of agricultural technology and equipment, Email: yujtong@163.com

Chunxiao Xing, PhD, research interest: recycling agriculture technology and equipment, Email: xcx@xjau.edu.cn

Published: 2026-06-30 doi: 10.25165/j.ijabe.20261903.10246

Outline

Abstract

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To address the issue of insufficient accuracy in the discrete element simulation model for cotton stalk -residual film mixtures, this paper employs the Hertz-Mindlin model with the JKR contact model to calibrate the contact parameters. First, significant parameters affecting the angle of repose were identified using Plackett-Burman experiments. Subsequently, the optimal parameter range was determined in conjunction with the steepest climb test. A regression model was constructed using Box-Behnken experiments to optimize the parameters, yielding the optimal parameter combination: cotton stalk-residual film rolling friction coefficient of 0.46, residual film-residual film rolling friction coefficient of 0.31, residual film-steel rolling friction coefficient of 0.47, and residual film-residual film JKR surface energy of 0.41 J/m². Simulated pile-up tests were conducted on a mixture of cotton stalks and residual film using these optimal parameter combinations. The results showed that the error between the simulated and measured angle of repose was only 3.06%, validating the reliability of the parameters and providing a basis for research into the interaction characteristics between cotton stalks and residual film during film recovery.

Key words

cotton stalk-residual plastic film mixture / parameter calibration / angle of repose / discrete element method

Cite this Article

Jinming Li, Jiaxi Zhang, Yichao Wang, Jiangtong Yu, Chunxiao Xing. Parameter calibration of a discrete element model for a mixture of cotton stalks and residual film[J]. International Journal of Agricultural and Biological Engineering, 2026 , 19 (3) : 80 -88 . DOI: 10.25165/j.ijabe.20261903.10246

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1　Introduction

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In 2024, Xinjiang’s cotton production reached 5.686 Mt, yielding approximately 28.43 Mt of cotton straw^[1]. Rich in nitrogen, phosphorus, potassium, and trace elements, cotton straw represents a valuable resource. However, burning or discarding it leads to significant resource waste and environmental pollution^[2]. Current utilization methods for cotton straw include fertilization, feed conversion, raw material sourcing, substrate conversion, and fuel conversion. Specifically, fertilizing with cotton stalks can boost cotton yields by an average of about 10% per mu. Using stalk for feed reduces costs by 20%-40%. Fuel utilization enables the production of solid fuels, gasification, and power generation, while raw material applications range from construction materials and light industry to textile feedstock. Substrate utilization is primarily for edible fungus cultivation or growth media^[3]. In Xinjiang, the dominant method for cotton stalk utilization, accounting for over 50% of the total, is direct shredding and returning it to fields as fertilizer^[4]. However, existing combined machinery for shredding cotton stalks and recovering residual film mixes these materials during operation. This practice results in excessively high impurity levels in the recovered cotton stalks. Consequently, the recovered film is often unusable for direct processing, limiting its resource utilization potential. To thoroughly investigate the interaction mechanisms between residual film and cotton stalks, precise contact parameters for the cotton stalk-residual film mixture are essential. However, the complex interaction properties of this composite material, combined with the errors introduced by traditional physical measurement methods, have a significant impact on the accuracy of subsequent modeling and simulation. The Discrete Element Method (DEM), a microscopic approach that quantifies particle interaction mechanisms, offers an ideal solution for studying contact parameters between cotton stalks and residual film^[5]. Therefore, obtaining precise parameters through discrete element simulation not only provides a theoretical basis for understanding the interaction between cotton straw and residual film, but also lays a crucial foundation for developing more complex models of the cotton straw-residual film-soil complex.

The Discrete Element Method (DEM) has become a mature tool for studying the mechanical behavior of agricultural materials, with applications ranging from modeling single components to complex mixtures^[5]. Research focusing on single-material modeling has achieved considerable depth. For instance, Shi et al.^[6] developed a DEM bonding model for flexible flax stems and calibrated its parameters by simulating the shearing process. Du et al.^[7] constructed a DEM mechanical model of tea plant stems, conducting tensile and puncture tests. Zhang et al.^[8] used Xinjiang cotton stalks as their test material, employing EDEM software for experimental simulation, parameter calibration, and validation through crushing tests. Shu et al.^[9] focused on rapeseed residues at optimal maturity after combine harvesting. They utilized EDEM simulation software for contact parameter calibration of major components and performed DEM-CFD coupled gas-solid analysis of a cyclone separation and cleaning device for rapeseed combine harvesting, integrated with bench testing. Shen et al.^[10] investigated residual plastic film in cotton field tillage layers. Using EDEM software and the Hertz-Mindlin with Bonding contact model, they calibrated parameters for the film’s discrete element model. The model’s validity was confirmed by comparing stretching process states and strain curves from physical tests with simulation results. Li et al.^[11] proposed a multi-feature integrated analysis method for constructing discrete element models of film-like materials, considering flexible deformation, friction properties, and aerodynamic characteristics. They developed a residual film DEM model using the Shell model in Rocky simulation software and validated its reliability through material flow experiments. Liu et al.^[12] employed the Bonding-V2 model with API rapid filling technology to establish a DEM simulation model for the residual film-soil-root-straw composite system. Deng et al.^[13] developed a residual film DEM to investigate morphological changes during the operation of a tubular fertilizer applicator. Fang et al.^[14] created a DEM for residual film in the tillage layer, validated by tensile tests. Tian et al.^[15] used the Moving Element Method (MEM) to model corn stover-soil mixtures, calibrating contact parameters based on the angle of repose. Ma et al.^[16] applied DEM to develop a simulation model for corn stover-cow manure mixtures, validating parameters through uniaxial compression tests. Despite these advancements, which have laid a solid foundation for DEM applications in agriculture, systematic research on discrete element simulation and parameter calibration specifically for cotton stalk-residual film mixtures remains a significant gap.

This study precisely calibrates the discrete element (DEM) contact parameters for cotton stalk-residual film mixtures found in Xinjiang cotton fields. Combining physical experiments with EDEM simulations, we used the measured physical angle of repose as the primary response variable for calibration^[17]. A systematic optimization approach was implemented, incorporating Plackett-Burman screening to identify significant parameters, followed by the steepest ascent method to determine optimal parameter ranges. Finally, Box-Behnken response surface experiments were employed to establish the optimal parameter combination. The reliability of the calibrated parameters was validated through physical angle-of-repose tests. These research findings may serve as a reference for the development of a cotton stalk–residual film–soil complex model and for studies on the interaction characteristics between cotton stalks and residual film.

2　Materials and methods

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2.1　Test materials

The experimental materials for this study comprised a mixture of cotton stalks and residual plastic film collected from Xinjiang cotton fields after the autumn harvest. To prepare simulated samples, the collected mixture was first separated. The moisture content of cotton stalks was determined using a drying method; after drying, the stalks were sorted, and those measuring 30 mm in length were selected, as samples within this length range accounted for 42% of the total. The residual plastic film was thoroughly cleaned and cut into small strips. Following separation, the densities of both the cotton stalks and residual plastic film were measured individually. Figure 1 displays the prepared samples and their corresponding simulated models.

2.2　Test method

A combined approach of simulation and physical testing was employed to calibrate the relevant parameters of the cotton stalk-residual film mixture. Specifically, the physical testing of the mixture’s angle of repose was conducted using a dedicated angle-of-repose testing rig, which measured the actual mean angle of repose of the cotton stalk-residual film mixture^[18]. Simulation tests for the angle of repose of cotton stalk-residual flim mixtures were carried out using EDEM 2022 software. Subsequently, Design-Expert 13.0 software was utilized for a Plackett-Burman screening experimental design^[19]. Significance analysis was then performed on the Plackett-Burman test results to identify the parameters that significantly influenced the simulated angle of repose of the cotton stalk-plastic film mixture. The optimal range for these significant factors was determined through steepest ascent experiments. A regression model for the significant factors affecting the pile angle of the cotton stalk-residual film mixture was subsequently established using a Box-Behnken experimental design^[20]. The Optimization module was then employed to comprehensively optimize the parameters, resulting in the identification of the optimal parameter combination. Finally, simulation tests were conducted using this optimal parameter combination to compare the simulated angle of repose of the cotton stalk-residual film mixture with its actual measured angle of repose^[21], thereby validating the accuracy of the calibrated parameters.

2.3　Determination of intrinsic material parameters

2.3.1　Determination of intrinsic parameters of cotton stalks

Cotton stalks of the Xinluzao 66 variety were collected from Yuli County, Bayingolin Mongol Autonomous Prefecture, Xinjiang Uygur Autonomous Region, and used as experimental material. To accurately determine their physical and mechanical properties, ten stalk samples were randomly selected for processing and classification. During parameter measurement, the diameter at the midpoint of each stalk was first measured using a Vernier caliper. Moisture content was determined using an electronic balance and a drying oven. Subsequently, a universal testing machine was employed to conduct a three-point bending compression test on the stalks (apparatus illustrated in Figure 2a). The loading rate was set at 2 mm/min and maintained until specimen failure. Throughout the testing process, the universal testing machine recorded load-displacement data (curve depicted in Figure 2b). Concurrently, a Vernier caliper measured diameter deformation in both the compression direction and the perpendicular direction. This test was repeated 10 times. Mechanical parameters were calculated using Equation (1) and then averaged. The final measured mean shear modulus for the cotton stalk was 650 MPa.

$ \left\{\begin{aligned} & E=\frac{F{L}^{3}}{48I\delta }\\&I=\frac{b{h}^{3}}{12}\\&G=\frac{E}{2(1+\mu )}\end{aligned}\right. $

(1)

where, E is the elastic modulus, Pa; F is the applied load, N; L is the support span, m; I is the sectional moment of inertia, m⁴; δ is the deflection, m; b is the specimen width, m; h is the specimen height, m; G is the shear modulus, Pa; and μ is the Poisson’s ratio.

2.3.2　Determination of intrinsic parameters of residual film

To investigate the mechanical properties of the residual film, the film was first cleaned, dried, and cut into standard specimens. Subsequently, mechanical property testing was conducted in accordance with GB/T 1040.3-2006. Tensile tests were performed on the specimens using a TMS texture analyzer (apparatus illustrated in Figure 3). The test parameters were set as follows: a loading rate of 200 mm/min, with loading ceasing upon specimen fracture. Each test series was repeated 10 times to ensure data reliability. Finally, Poisson’s ratio, elastic modulus, and shear modulus were calculated using Equation (2). The results indicated an average shear modulus of 1.57 MPa for the residual film. The intrinsic parameters of cotton stalks and residual film are shown in Table 1.

$ \left\{\begin{aligned} & E=\frac{\sigma }{\varepsilon }\\& \sigma =\frac{F}{{A}_{0}}\\& \varepsilon =\frac{\Delta L}{{L}_{0}}\\& G=\frac{E}{2(1+\mu )}\end{aligned}\right. $

(2)

where, E is the elastic modulus, Pa; δ is the stress, Pa; ε is the strain; F is the tensile load, N; ΔL is the specimen elongation, m; L₀ is the original gauge length of the specimen, m.

2.4　Contact parameter determination

2.4.1　Determination of static friction coefficient between cotton stalk and steel plate

This study aims to determine the static friction coefficient between cotton stalks and between cotton stalks and steel. Experiments were conducted using a homemade inclined plane apparatus. During testing, cotton stalks were placed on the base plate of the apparatus, and the incline angle was gradually increased until the sample stalks were on the verge of slipping. The critical angle at this point was recorded^[22]. Each set of experiments was repeated 10 times. The average measured angle was then substituted into Equation (3) to calculate the static friction coefficient.

$ \mu =\tan \varphi $

(3)

where, μ represents the coefficient of static friction; φ denotes the angle of inclination of the inclined plane during sliding, (°).

To determine the static friction coefficient between cotton stalks, the base plate of the inclined plane apparatus was covered with cotton stalks, and the aforementioned test procedure was repeated. The static friction coefficient between cotton stalks and steel was measured to be 0.40, while that between cotton stalks alone was 0.51.

2.4.2　Determination of rolling friction coefficient between cotton stalks and steel plate

To determine the rolling friction coefficient between cotton stalks and a steel plate, this study employed the inclined plate rolling method. An experimental platform, as illustrated in Figure 4, was constructed for this purpose. During testing, the steel inclined plate was first fixed at a specific angle θ. A cotton stalk sample was then released from rest at a vertical height H above the inclined surface^[22]. After the sample rolled down the incline and came to rest on the horizontal plate, its rolling distance S on the horizontal plate was precisely measured. This distance was subsequently used to calculate the rolling friction coefficient.

If the tilt angle θ and slope length L are excessively large, the sample is prone to bounce during rolling, which can compromise the accuracy of the results. Conversely, if these parameters are too small, the horizontal rolling distance becomes unacceptably short, leading to an increased relative measurement error. Assuming the sample undergoes purely rolling motion solely under the influence of rolling friction, the law of conservation of energy yields:

$ GH={\mu }_{f}G\left(L\cos \theta +S\right) $

(4)

where, μ_f is the rolling friction coefficient between cotton stalks and steel plate; G is the gravitational force of cotton stalks, N.

The test was repeated 10 times, and the average values were calculated. The measured rolling friction coefficient between cotton stalks and steel was found to be 0.06, while the coefficient between cotton stalks themselves was 0.2.

3　Angle of repose simulation test

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3.1　Contact model selection

The adhesion observed between cotton stalks and residual film stems from the film’s inherent static properties and the fragmentation of cotton stalks after shredding and their return to the field. The Hertz-Mindlin with JKR contact model is capable of representing the mutual attraction between particles^[23]. Consequently, this study utilizes the Hertz-Mindlin with JKR Cohesion (JKR) model to construct a discrete element model for the cotton stalk-residual film mixture. Contact occurs due to particle motion, during which particle surfaces gradually deform to generate contact forces. The normal elastic contact force, F_JKR, within the JKR model is dependent on the overlap, δ, the interaction parameter, γ, and the surface energy. It is calculated as follows:

$ \left\{\begin{aligned} & {F}_{\rm JKR}=-4\sqrt{\pi \gamma {E}^{*}}{\alpha }^{\tfrac{3}{2}}+\frac{4{E}^{*}}{3{R}^{*}}{\alpha }^{3}\\&\delta =\frac{{\alpha }^{2}}{{R}^{*}}-\sqrt{\frac{4\pi \gamma \alpha }{{E}^{*}}}\end{aligned}\right. $

(5)

Among them:

$ \frac{1}{{E}^{*}}=\frac{1-{v}_{1}^{2}}{{E}_{1}}+\frac{1-{v}_{2}^{2}}{{E}_{2}} $

(6)

$ {R}^{*}=\frac{1}{{R}_{1}}-\frac{1}{{R}_{2}} $

(7)

where, F is the normal elastic force in the JKR model, N; δ is the normal overlap between two contacting particles, m; α is the tangential overlap between two contacting particles, m; γ is the surface energy, N/m; E^* is the equivalent Young’s modulus, Pa; R^* is the equivalent contact radius, m; v₁ and v₂ are the Poisson’s ratios of the two particles; E₁ and E₂ are the shear moduli of the two contacting particles, Pa; R₁ and R₂ are the radii of the two contacting particles, m.

When the surface energy γ = 0, the normal force F_n in the F_JKR model is equal to that in the Hertz-Mindlin contact model:

$ {F}_{\rm JKR}={F}_{n}=\frac{4}{3}{E}^{*}\sqrt{{R}^{*}}{\delta }^{\tfrac{3}{2}} $

(8)

If particles are not in direct contact, the JKR model can also provide attractive cohesive forces^[24], with the maximum gap for non-zero cohesive forces between particles being:

$ \delta _{c}^{}=\frac{{\alpha }_{c}^{2}}{{R}^{\ast }}-\sqrt{\frac{4\text{π} \gamma {\alpha }_{c}}{{E}^{\ast }}} $

(9)

$ {\alpha }_{c}={\left[\frac{9\text{π} \gamma {R}^{\ast }}{2{E}^{\ast }}-\left(\frac{3}{4}-\frac{1}{\sqrt{2}}\right)\right]}^{\tfrac{1}{3}} $

(10)

where, δ_c represents the maximum normal gap between particles when non-zero cohesive forces exist, m; α_c denotes the maximum tangential gap between particles when non-zero cohesive forces exist, m.

When δ > δ_c, the cohesive force between particles becomes zero.

When particles are not in actual contact and the separation equals δ_c, the cohesive force reaches its maximum value.

$ {F}_{pull{\text{-}}off}=-\frac{3}{2}\text{π} \gamma {R}^{\ast } $

(11)

where, F_pull-off is the cohesive force between two particles, N.

3.2　Simulation model development

3.2.1　Physical tests on angle of repose

To determine the angle of repose parameters for the cotton stalk-residual film mixture, this study developed a physical testing platform, as illustrated in Figure 5. The platform is principally composed of a hopper, a support frame, and a horizontal steel plate. During the test, the mixed material was loaded into the hopper and allowed to fall freely under gravity, forming a pile on the steel plate surface^[25]. After the material pile reached a stable configuration, an angle measuring instrument was employed to record its naturally formed angle of repose. To ensure data reliability, the experiment was replicated 10 times independently, and the arithmetic mean of the measurement results was calculated. The statistical analysis revealed that the angle of repose for this mixed material is 31.59°.

3.2.2　Simulation model establishment and EDEM parameter configuration

This study investigates the pile formation behavior of cotton stalk-residual film mixtures through numerical simulation using the EDEM software. The simulation employs the Hertz-Mindlin with JKR contact model. To strike a balance between simulation efficiency and model fidelity, cotton stalks were simplified into a model that replicates their physical dimensions, represented as a collection of circular particles. To accurately capture the flexible mechanical properties of residual film, it was modeled as strip-like elements and constructed using the bonding model. The geometric configuration of the simulation environment, including the hopper and steel plate, precisely mirrored the physical test setup. Particles were introduced at a rate of 5 kg/s via a particle generator, with a mass ratio of 77.19% cotton stalks to 22.81% residual film. The total simulation duration was 6.5 seconds, with the time step set to 20% of the Rayleigh time step and the mesh size set to three times the particle radius^[26]. Once the particles formed a stable pile under gravity (as illustrated in Figure 6), Matlab-based image processing techniques were utilized on the simulation screenshots for binarization and contour line extraction^[27]. Finally, linear fitting of the extracted contour data using Origin software yielded the simulated angle of repose for this mixed material. The physical parameter ranges for the cotton stalk-residual film mixture were determined based on preliminary experiments and referencing parameter ranges from studies^[8,10,13,14], as detailed in Table 2.

4　Simulation tests and results analysis of residual film-cotton stalk mixtures

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4.1　Plackett-Burman test and significance analysis

To rapidly identify the key factors influencing the angle of repose of cotton stalk-residual film mixtures, this study utilized the Plackett-Burman design method^[26]. Experiments were designed and analyzed using Design-Expert, with the mixture’s angle of repose serving as the response variable. This method assesses significance by comparing the differences in main effects across two levels for each factor. Table 3 lists the level codes for the experimental factors (X₁-X₁₀), while Tables 4 and 5 provide detailed experimental design schemes, results, and analyses of variance.

According to the ANOVA results in Table 5, four parameters significantly influenced the mixture’s angle of repose (p<0.05) among all investigated factors: the cotton stalk-residual film rolling friction coefficient (X₃), residual film-residual film rolling friction coefficient (X₆), residual film-steel rolling friction coefficient (X₈), and residual film-residual film JKR surface energy (X₁₀). The cumulative contribution rate of these four factors reached as high as 91.89%^[28], making them the dominant factors influencing changes in the angle of repose. Consequently, these four parameters were selected for subsequent steep slope climbing tests.

To visually assess the influence of each factor, graphical analysis was performed on the Plackett-Burman experimental results, yielding a semi-normal probability effect plot (Figure 7a) and a Pareto chart (Figure 7b). In the semi-normal probability effect plot, the distance of effect points from the fitted line reflects their significance. Figure 7a shows that the effect points for X₆ (Residual Film-Residual Film Rolling Friction Coefficient) and X₁₀ (Residual Film-Residual Film JKR Surface Energy) deviate significantly from the fitted line, indicating highly significant positive effects on the angle of repose, with X₆ being more significant than X₁₀. The Pareto chart (Figure 7b) further validates and supplements this conclusion. It shows that the standardized effect values for factors X₃, X₆, X₈, and X₁₀ all exceed the significance threshold (t-value), reaffirming their significant positive influence on the angle of repose. Based on this analysis, these four significant factors were selected for subsequent steepest climb tests. The remaining non-significant factors will be fixed at their central levels: X₁=0.4, X₂=0.35, X₄=0.54, X₅=0.55, X₇=0.52, and X₉=0.3.

4.2　Steepest climb test design

Test results indicate a positive correlation between increasing levels of the four factors and the angle of repose. Concurrently, the relative error between simulated and experimental values exhibits a gradually increasing trend. At test group 1 (X₃=0.2, X₆=0.2, X₈=0.2, X₁₀=0.3 J/m²), the relative error reached its minimum value of 4.18%, suggesting that the optimal parameter combination lies near this point. To achieve more precise optimization within this region, a Box-Behnken design (BBD) was employed for response surface analysis. Integrating the results from test groups 2 and 3, a new central point was selected near the minimum error point: cotton stalk-residual film rolling friction coefficient X₃=0.35, residual film-residual film rolling friction coefficient X₆=0.3, residual film-steel rolling friction coefficient X₈=0.35, and residual film-residual film JKR surface energy X₁₀=0.4 J/m². This point served as the basis for the subsequent four-factor, three-level experimental design, the experimental schedule is shown in Table 6.

4.3　Box-Behnken experimental design

To precisely investigate the nonlinear relationship between the four significant factors (X₃, X₆, X₈, X₁₀) and the angle of repose, this study employed the Box-Behnken design (BBD) method^[29]. Design-Expert software was utilized for experimental design and data analysis. Based on the experimental results, a quadratic polynomial regression model was constructed with the angle of repose as the response variable. Detailed factor coding, the experimental design plan, and the response results are presented in Tables 7 and 8, respectively.

4.4　Regression model

Multivariate regression analysis was performed on the experimental data to establish a second-order regression model relating the angle of repose of the residual film-cotton stalk mixture to the four significant parameters. The equation is as follows:

$ \begin{split} Y=&29.35+1.96{X}_{3}-2.06{X}_{6}+3.74{X}_{10}-2.29{X}_{3}{X}_{8}-2.41{X}_{3}{X}_{10}-\\& 2.58{X}_{6}{X}_{10}-2.75{X}_{8}{X}_{10}+1.63{X}_{6}^{2}+2.86{X}_{8}^{2}\\[-1pt]\end{split} $

(12)

Table 9 presents the results of the variance analysis for the regression model. These findings demonstrate that the model is highly significant (p<0.0001). With a coefficient of determination (R²) of 0.9034, the model exhibits an excellent goodness-of-fit. Furthermore, the interaction terms X₃X₈, X₃X₁₀, X₆X₁₀, and X₈X₁₀ were found to significantly influence the angle of repose (p<0.05). The model’s coefficient of variation (CV) of 5.73% indicates high precision and reliability in the experiment.

4.5　Interaction effects in the regression model

To intuitively analyze the impact of significant interaction terms on the angle of repose, response surface analysis plots were generated based on the regression equations (Figure 8). Figure 8a response surface shows a steeper slope in the X₃ direction than in the X₈ direction, indicating the stronger influence of X₃ as compared to X₈. In Figure 8b, the contour lines are denser along the X₁₀ direction than along X₃, forming a distinct elliptical shape, which signifies the greater influence of X₁₀ than X₃. Similarly, Figures 8c and 8d demonstrate that X₁₀ also exerts a stronger effect on the angle of repose than X₆ and X₈. Collectively, the effects of all four interaction terms on the angle of repose were found to be significant (p<0.05). The order of interaction effect strength is as follows: X₈X₁₀ > X₆X₁₀ > X₃X₁₀ > X₃X₈.

4.6　Optimization of residual film-cotton stalk blending parameters and model validation

4.6.1　Objective function and constraints

Within the specified factor level range, parameters were optimized using the Design-Expert software’s optimization function. The model was solved with a target value of 31.59°, and multiple solution sets were simulated for verification. The solution set that most closely matched the physical test geometry was selected^[30], yielding the following values: cotton stalk-residual film rolling friction coefficient: 0.46, residual film-residual film rolling friction coefficient: 0.31, residual film-steel rolling friction coefficient: 0.47, residual film-residual film JKR surface energy: 0.41 J/m².

4.6.2　Angle of repose verification test

The optimal parameters were set in EDEM, with other contact parameters configured at intermediate levels^[31]. Figure 9 displays the discrete element simulation of the cotton stalk-residual film mixture’s angle of repose. After repeating the test 10 times, the average simulated angle of repose was found to be 32.59°, with a relative error of 3.06% compared to the actual angle of repose. These results confirm the reliability of the calibrated contact parameters for the cotton stalk-residual film mixture.

5　Conclusions

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This study utilized physical testing methods, including inclined plane, three-point bending, and tensile load tests, to determine specific values for the coefficient of friction and coefficient of restitution. For parameters difficult to measure experimentally, their numerical ranges were established through a literature review. A custom-built test rig was employed to measure the angle of repose of the cotton stalk-residual film mixture. Using the angle of repose as the response variable, a significance analysis, screening, and optimization of the physical parameters for the cotton stalk-residual film mixture were performed using Plackett-Burman design, the steepest ascent method, and Box-Behnken response surface analysis. A simulation model for the angle of repose was then established based on the optimized parameters and validated against physical test results to verify the accuracy of the calibrated parameters. The specific conclusions of this study are as follows:

(1) For the discrete element simulation parameter calibration of the cotton stalk-residual film mixture, Plackett-Burman results indicate that the rolling friction coefficient between cotton stalks and residual film, the rolling friction coefficient between residual films, the residual film-to-steel rolling friction coefficient, and the residual film-to-residual film JKR surface energy significantly influence the mixture’s angle of repose. Other simulation parameters showed no significant effect on the angle of repose.

(2) The secondary multiple regression model for the cotton stalk-residual film mixture exhibited reliable performance, as confirmed by results from steepest climb tests and Box-Behnken response surface experiments. The model identified the following parameter combinations as significantly influencing the mixture’s angle of repose: cotton stalk-residual film rolling friction coefficient: 0.46; residual film-residual film rolling friction coefficient: 0.31; residual film-steel rolling friction coefficient: 0.47; residual film-residual film JKR surface energy: 0.41 J/m².

(3) EDEM simulation tests, utilizing calibrated parameters, yielded a simulated pile angle of 32.59° for the cotton stalk-residual film mixture, exhibiting a 3.06% deviation from the actual pile angle. Optimized calibration parameters can be employed to simulate the contact parameters of this mixture. It should be noted that the discrete element simulation model for the cotton stalk-residual film mixture established in this study shows certain discrepancies with the physically tested angle of repose. This discrepancy may arise from the simplification of cotton stalks into a uniform particle composition during model development, whereas actual cotton stalks possess distinct mechanical properties between their outer skin and inner core. Modeling with a single particle type inherently introduces errors. Therefore, future research could involve simulating the outer skin and inner core of cotton stalks using particles with distinct material properties, thereby creating a cotton stalk-residual film mixture model that more accurately reflects real-world conditions. Compared to Shen et al.^[10] and Li et al.^[11], who modeled single-component plastic film waste, this study focuses primarily on calibrating the contact parameters for a mixture of plastic film and cotton stalks, and validates the model. This will provide a reference for future studies on the interaction between cotton straw and residual film during the recovery process, and for the establishment of a residual film–cotton straw–soil complex.

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doi: 10.25165/j.ijabe.20261903.10246

Receive Date：2025-10-03
Online Date：2026-08-27
Published：2026-06-30

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Received：2025-10-03
Accepted：2026-05-31

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College of Mechanical and Electrical Engineering, Xinjiang Agricultural University, Urumqi 830052, China

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Jiaxi Zhang, Professor, research interest: recycling of agricultural technology and equipment. College of Mechanical and Electrical Engineering, Xinjiang Agricultural University, Urumqi 830052, China. Tel: +86-13899961137, Email: zhangjiaxi@xjau.edu.cn.

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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Table 1 Material intrinsic parameters

Parameters	Value
Cotton stalk Poisson’s ratio	0.35
Cotton stalk shear modulus/MPa	650
Residual film Poisson’s ratio	0.32
Residual film shear modulus/MPa	1.57
Steel Poisson’s ratio	0.3
Steel shear modulus/MPa	7.8×10⁴
Steel density/kg·m^–3	7850

Table 2 Simulation parameters for the angle of repose of a mixture of residual film and cotton stalk

Parameters	Values
Cotton stalk-cotton stalk recovery coefficient	0.5
Cotton stalk-static friction coefficient of cotton stalk	0.51
Cotton stalk-rolling friction coefficient of cotton stalk	0.2
Cotton stalk-steel recovery coefficient	0.5
Cotton stalk-static friction coefficient of steel	0.4
Cotton stalk-rolling friction coefficient of steel	0.06
Cotton stalk-residual film recovery coefficient X₁	0.3-0.5
Cotton stalk-residual film static friction coefficient X₂	0.15-0.55
Cotton stalk-residual film rolling friction coefficient X₃	0.2-0.8
Residual film-residual film recovery coefficient X₄	0.34-0.74
Residual film-residual film static friction coefficient X₅	0.25-0.85
Residual film-residual film rolling friction coefficient X₆	0.2-0.6
Residual film-static friction coefficient of steel X₇	0.32-0.72
Residual film-rolling friction coefficient of steel X₈	0.2-0.8
Cotton stalk-residual film JKR surface energy X₉/J·m^–2	0.1-0.5
Residual film-residual film JKR surface energy X₁₀/J·m^–2	0.3-0.7

Table 3 Plackett-Burman test factors and codes

Factor	Code
Factor	–1	0	1
Cotton stalk-residual film recovery coefficient X₁	0.3	0.4	0.5
Cotton stalk-residual film static friction coefficient X₂	0.15	0.35	0.55
Cotton stalk-residual film rolling friction coefficient X₃	0.2	0.50	0.8
Residual film-residual film recovery coefficient X₄	0.34	0.54	0.74
Residual film-residual film static friction coefficient X₅	0.25	0.55	0.85
Residual film-residual film rolling friction coefficient X₆	0.2	0.4	0.6
Residual film-static friction coefficient of steel X₇	0.32	0.52	0.72
Residual film-rolling friction coefficient of steel X₈	0.2	0.5	0.8
Cotton stalk-residual film JKR surface energy X₉/J·m^–2	0.1	0.3	0.5
Residual film-residual film JKR surface energyX₁₀/J·m^–2	0.3	0.4	0.7

Table 4 Plackett-Burman test design and results

Test No.	Factor											Angle of repose/(°)
Test No.	X₁	X₂	X₃	X₄	X₅	X₆	X₇	X₈	X₉	X₁₀	K	Angle of repose/(°)
1	1	1	–1	–1	–1	1	–1	1	1	–1	1	33.68
2	–1	1	1	–1	1	1	1	–1	–1	–1	1	31.88
3	–1	1	1	1	–1	–1	–1	1	–1	1	1	32.89
4	–1	–1	–1	1	–1	1	1	–1	1	1	1	34.88
5	–1	1	–1	1	1	–1	1	1	1	–1	–1	28.07
6	1	1	1	–1	–1	–1	1	–1	1	1	–1	32.13
7	–1	–1	1	–1	1	1	–1	1	1	1	–1	35.72
8	1	–1	1	1	–1	1	1	1	–1	–1	–1	34.21
9	–1	–1	–1	–1	–1	–1	–1	–1	–1	–1	–1	25.12
10	1	–1	1	1	1	–1	–1	–1	1	–1	1	27.44
11	1	1	–1	1	1	1	–1	–1	–1	1	–1	34.18
12	1	–1	–1	–1	1	–1	1	1	–1	1	1	29.23

Table 5 ANOVA result

Parameters	Effect	F-value	p-value	Contribution	Order of significance
X₁	0.39	16.42	0.1540	0.36	8
X₂	1.04	119.46	0.0581	2.59	5
X₃	1.52	255.44	0.0398*	5.54	3
X₄	0.65	47.05	0.0922	1.02	7
X₅	–1.07	125.68	0.0566	2.72	10
X₆	4.95	2709.48	0.0122*	58.72	1
X₇	0.23	5.78	0.2510	0.13	9
X₈	1.36	205.44	0.0443*	4.45	4
X₉	0.74	59.86	0.0818	1.30	6
X₁₀	3.11	1068.26	0.0195*	23.15	2

Table 6 Test design and results of the steepest climb

Test No.	X₃	X₆	X₈	X₁₀	Angle of repose/(°)	Relative error/%
1	0.2	0.2	0.2	0.3	30.27	4.18
2	0.35	0.3	0.35	0.4	33.94	7.44
3	0.5	0.4	0.5	0.5	34.25	8.42
4	0.65	0.5	0.65	0.6	36.68	16.11
5	0.8	0.6	0.8	0.7	37.59	18.99

Table 7 BBD test factors and levels coding

Code	Factor
Code	X₃	X₆	X₈	X₁₀/J·m^–2
–1	0.2	0.2	0.2	0.3
0	0.35	0.3	0.35	0.4
1	0.5	0.4	0.5	0.5

Table 8 BBD experimental design and results

Test No.	Factor				Angle of repose/(°)
Test No.	X₃	X₆	X₈	X₁₀	Angle of repose/(°)
1	–1	–1	0	0	27.33
2	–1	0	1	0	33.87
3	0	1	0	1	30.58
4	0	–1	0	–1	27.25
5	0	0	0	0	26.53
6	0	0	–1	1	39.54
7	1	–1	0	0	37.63
8	0	0	1	–1	31.97
9	0	0	–1	–1	25.92
10	1	0	0	1	34.83
11	0	0	1	1	34.59
12	0	0	0	0	29.94
13	0	–1	1	0	35.83
14	1	0	1	0	31.92
15	0	–1	0	1	39.77
16	0	0	0	0	31.98
17	1	0	–1	0	38.63
18	0	1	0	–1	28.36
19	0	0	0	0	27.56
20	1	0	0	–1	32.71
21	0	0	0	0	30.72
22	–1	1	0	0	27.87
23	–1	0	–1	0	31.43
24	–1	0	0	1	37.54
25	1	1	0	0	31.61
26	0	1	1	0	30.54
27	0	1	–1	0	30.45
28	–1	0	0	–1	25.78
29	0	–1	–1	0	36.28

Table 9 Analysis of variance of regression model

Source	Sum of squares	df	Mean square	F-value	p-value
Note: significant (p<0.05); *highly significant (p<0.01).
Model	440.99	14	31.50	9.35	<0.0001	**
X₃	46.06	1	46.06	13.68	0.0024	**
X₆	50.76	1	50.76	15.07	0.0017	**
X₈	1.04	1	1.04	0.3084	0.5874
X₁₀	167.70	1	167.70	49.80	<0.0001	**
X₃X₆	10.76	1	10.76	3.19	0.0955
X₃X₈	20.93	1	20.93	6.22	0.0258	*
X₃X₁₀	23.23	1	23.23	6.90	0.0199	*
X₆X₈	0.0729	1	0.0729	0.0216	0.8851
X₆X₁₀	26.52	1	26.52	7.88	0.0140	*
X₈X₁₀	30.25	1	30.25	8.98	0.0096	**
$ X_3^2 $	17.19	1	17.19	5.10	0.0403	*
$ X_6^2 $	2.93	1	2.93	0.8688	0.3671
$ X_8^2 $	52.88	1	52.88	15.70	0.0014	**
$ X_{10}^2 $	11.63	1	11.63	3.45	0.0842
Residual	47.14	14	3.37
Lack·of fit	26.84	10	2.68	0.5290	0.8112
Pure error	20.30	4	5.07
Cor total	488.13	28

Figure 1 Cotton stalk-residual film mixed material

Figure 2 Determination of cotton stalk characteristic parameters

Figure 3 Determination of residual film characteristic parameters

Figure 4 Rolling friction coefficient measurement

Figure 5 Simulation model of stacking angle

Figure 6 Fitting of the angle of repose profile

Figure 7 Effect analysis

Figure 8 Interaction response surface plot

Figure 9 Comparison of physical test and simulation test of stacking angle

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