Research on the discrete element modeling method and tensile fracture behavior of the control unit stranded wire of Shearer cables | Scientific Reports

Apr 06, 2025

Scientific Reports volume 15, Article number: 11756 (2025) Cite this article

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In addressing the mechanical response of the complex twisted structure of the control unit stranded wire of shearer cables, a modeling method based on Discrete Element Method (DEM) is proposed. This method incorporates nonlinear plastic deformation and the complex multi-body contact characteristics caused by twisting. In this study, a three-dimensional spatial model of the control unit stranded wire was developed and discretized into a discrete element model. Axial tensile loads were applied to the model, causing fracture, and the resulting stress-strain curve was compared with experimental tensile test results to validate the feasibility and accuracy of the discrete element model. Based on this model, the mechanical response of the control unit stranded wire under various factors, such as pitch and copper wire diameter, was studied. The results indicate that the stress-strain curves of the control unit stranded wire exhibit consistent trends across four different kinds of pitch. When the copper wire diameter was 0.39 mm and the pitch was 39 mm, 44 mm, 49 mm, and 54 mm, the corresponding tensile strengths were 294.00 MPa, 282.12 MPa, 268.56 MPa, and 266.16 MPa, respectively, while the fracture elongation rates were 26.94%, 26.24%, 25.84%, and 25.53%. Smaller pitch resulted in higher tensile strength and greater fracture elongation. When the pitch was greater than or equal to 49 mm, the influence of the pitch on the stress-strain curve diminished. When the pitch was 39 mm and the copper wire diameters were 0.25 mm, 0.30 mm, and 0.39 mm, the corresponding tensile strengths were 263.46 MPa, 272.58 MPa, and 294.00 MPa, and the fracture elongation rates were 23.93%, 24.49%, and 26.94%, respectively. Larger copper wire diameters led to higher tensile strength and greater fracture elongation. The stress-strain curves for wire diameters of 0.25 mm and 0.30 mm were relatively similar, while for a diameter of 0.39 mm, both the tensile strength and fracture elongation rate increased significantly, with the fracture elongation rate increasing by 12.58% compared to the 0.25 mm diameter. The study shows that smaller pitch and larger copper wire diameters result in higher fracture elongation rates and better ductility. The corresponding fitting curves are also provided. This research offers theoretical support and new insights for the study of the mechanical response of complex twisted structures.

Shearer cables, which are essential for power and signal transmission1, face significant mechanical demands due to the continuous movement and frequent bending during operation. The complex operating conditions often result in failures such as core breakage in the control unit of cable, which negatively impacts the cable’s lifespan and mining efficiency. Therefore, studying the mechanical response of the control unit stranded wire is crucial for enhancing their performance and extending their service life. The traditional finite element model based on the classical continuum elastoplastic constitutive theory is a common tool for investigating the mechanical behaviors of twisted structures2. Eduardo A.W de Menezes et al.3 compared three cable modeling approaches—beam elements, solid elements, and the explicit dynamic model—and found that the dynamic display model can accurately represent the global behavior of the cable, making the construction of more complex cable structures possible. Jiang4developed a mechanical analysis model for the Rutherford-type superconducting cable under the basic deformation modes and analyzed the effects of factors such as the friction factor, conductor winding angle, and core structure on the cable’s mechanical behavior. Xia et al.5developed a parametric modeling approach to construct triangular strand steel wire ropes with a defined range of pitch. They compared the mechanical performance differences under tensile loads for different pitch and validated the accuracy of the finite element model through tensile testing. In the finite element studies mentioned above, the twisted structure was analyzed using finite element analysis. The complex contact interactions, mesh distortion, and high computational cost of the twisted structure led to the adoption of simplified models, where the smallest modeling unit was represented by stranded wire in a three-dimensional model (The stranded wires are composed of copper wires twisted together). However, the mechanical response of the simplified model differs from that of the actual structure.

To study the more accurate mechanical response of the stranded wire, it is necessary to make up the single copper wire as the smallest modeling unit and apply axial loads to induce fracture. Due to its mesh-free nature, DEM does not require consideration of deformation conditions, making it widely used for addressing issues such as local contact, damage, and fracture6,7. Jia8 developed a multi-layer discrete element dynamic model based on DEM to accurately predict the mechanical behavior of superconducting cables at different levels of twisting. This model analyzed the macroscopic mechanical properties of superconducting cables under the influence of various factors, including pitch, lateral cyclic compression, and liquid helium mass flow rate. Chen et al.9 simulated tensile tests of high-carbon steel using DEM and found that the particle radius expansion algorithm could discretize continuous models into homogeneous materials. The bonding model was able to simulate multiple bond failures during tensile tests, leading to fracture. The results indicated that both the particle physical radius and contact radius significantly affected the ultimate stress and Young’s modulus. Guo et al.10 proposed an elastoplastic model based on DEM for simulating metal wires and plastic fibers and derived a fiber deformation model related to loading history from the stress-strain relationship of fiber materials. DU et al.11 developed a discrete element model for the 1 × 7 wire strand structure and applied axial loads to analyze the impact of different helical angles on the mechanical behavior of the steel wire rope. They found that an increase in helical angle resulted in higher equivalent Young’s modulus and axial deformation of the outer steel wires.

The control unit stranded wire of shearer cables is formed by twisting copper wires together according to specific specifications and processes. The complex internal contacts complicate the analysis of their mechanical response. The discrete element method, based on the contact force-displacement constitutive relations, offers significant advantages in addressing issues involving continuous and discrete interactions, multi-body contact, and local large deformations12. This study employed DEM to develop the three-dimensional spatial model and the discrete element model of the Control Unit Stranded wire of shearer cables, considering their nonlinear plastic deformation. The fracture behavior of the cables under axial tensile load was analyzed, and the validity of the discrete element model was verified through tensile testing. Furthermore, the influence of the pitch and the copper wire diameter on the mechanical behavior of the control unit cables was investigated.

The control unit stranded wire with a cross-sectional area of 4 mm² (denoted as KA4) was selected as the research subject. According to the manufacturing process, the KA4 control unit stranded wire consists of 34 wires of 0.39 mm copper wire, twisted in a three-layer configuration with a threading pattern of 5 + 11 + 18. The copper wires exhibit continuous characteristics, while the contact between them demonstrates discrete features. Therefore, the key to constructing an accurate discrete element numerical model for the control unit stranded wire lies in how to discretize the continuous copper wires and define the interactions between the wires to precisely represent the continuity and discreteness observed after the wires are twisted.

The first step is to establish the spiral spatial geometric model of the copper wire twisting. When using Creo software to create the control unit stranded wire, it is essential to determine the helical centerline of each layer of copper wire to improve both modeling efficiency and accuracy, as shown in Fig. 1.

Centerline of the copper wire helix in the twisted control unit strand.

A cylindrical coordinate system is established, and the helical trajectory equations for the center of the copper wire in each layer of the control unit are determined through the curve equation13:

In the equation, r represents the twisting radius of the copper wire (mm); theta is the angle between the line connecting the origin of the cylindrical coordinate system and the origin of the Cartesian coordinate system and the x-axis (°); L is the length of the control unit stranded wire (mm); t is the independent variable that varies from 0 to 1; h is the pitch of the control unit stranded wire (mm); D is the outer diameter of the control unit stranded wire (mm); m is the lay ratio of the control unit stranded wire.

Using the trajpar function14, the scanning trajectory of each layer of copper wire is plotted. The function, as shown in Eq. (3), generates a trajectory where the scanning section rotates around the trajectory while moving along it. This process is used to visualize the twisting structure of the control unit stranded wire.

In the equation, sd represents the rotation angle of the section around the scanning trajectory (°); \(\alpha\)is the initial rotation angle of the section around the scanning trajectory (°); trajpar is the scanning trajectory parameter, representing the percentage of the feature relative to the trajectory length.

The above helical equation can be used to generate a 3D spatial model of the control unit stranded wire, as shown in Fig. 2. This model consists of three layers of twisted copper wires, with the cross-section shown in Fig. 2(b).

Schematic of the 3D spatial model of the control unit stranded wire.

The spatial 3D model of the control unit stranded wire was constructed based on the aforementioned method. This section described its discretization process. To accurately represent the structural characteristics of the control unit stranded wire, the positions of the center points of each copper wire were extracted from the 3D model and saved in a text file. Spherical particles with identical material properties were selected, where the diameter of each particle matched that of a single copper wire (0.39 mm). The model was then compiled using the FISH language in PFC3D software, arranging the particles along the centerline of the twisted copper wire. Neighboring spheres were connected by adhesive bonds to complete the discretization of the control unit stranded wire, as shown in Fig. 3. The adhesive bonds can withstand various types of loads, allowing the constructed discrete element model to accurately simulate the mechanical behavior of the control unit stranded wire under loads.

Discretization process of the control unit stranded wire.

DEM offers significant advantages in studying the mechanical properties of continuous media by treating each discrete particle as part of the continuum and applying force-displacement control between particles to maintain the continuity of the discrete particle system. The contact model between force and displacement during the motion of two particles is the fundamental model used in discrete dynamic simulation programs. By incorporating the force-displacement equation, the elastic-plastic behavior between particles can be accurately simulated.

During the collision and contact process between the spherical particles composing the copper wire, the contact surfaces undergo plastic deformation. The commonly used elastic contact models are insufficient to accurately describe these contact characteristics. In elastoplastic models, a piecewise approach is typically used to describe the contact behavior, employing different force-displacement constitutive equations for the elastic, elastoplastic, and loading-unloading stages. When two spheres come into contact, as shown in Fig. 4, the normal stiffness coefficient in the elastic stage is given by15:

\({E^*}\) and \({R^*}\) are the equivalent elastic modulus and equivalent radius between the two spheres, respectively. Their expressions are given by Eqs. (5) and (6)15:

Where \({E_i}\)、\({E_j}\)、\({\nu _i}\)、\({\nu _j}\)、\({R_i}\)and\({R_j}\)represent the elastic modulus, Poisson’s ratio, and radius of the sphere, respectively.

Contact model between discrete element particles.

The Thornton elastoplastic contact model16 is based on the Hertz contact model and incorporates plastic deformation at the contact point to provide the force-displacement equation for the elastoplastic contact process of spheres. This method divides the collision process into the loading and unloading stages. During the loading stage, the effect of material deformation beyond the yield strength is primarily considered, while the unloading stage focuses on the influence of residual deformation at the contact point.

When plastic deformation occurs at the contact surface during the collision loading stage, the contact surface is divided into two regions: elastic and plastic, as shown in Fig. 5. a represents the radius of the contact surface, \({a_p}\) is the radius of the plastic deformation region on the contact surface, and \({a_c}\) is the critical contact radius at the point of initial yielding.

Schematic of the stress distribution on the contact surface.

The contact force in the plastic deformation region is given by12:

Where \({\delta _n}\) is the deformation of the sphere after the collision, and \({\delta _c}\) is the critical deformation at the point of yielding on the contact surface. The relationship between \({\delta _c}\) and the yield strength can be determined through the material’s yield strength and Eqs. (5) and (6), as given by:

During the unloading stage, the plastic deformation at the contact surface caused by the loading stage leads to a change in the equivalent radius\(R_{r}^{*}\). At the end of unloading, a residual deformation \({\delta _r}\)remains, and the normal stiffness at this point is given by:

The residual deformation can be determined by the maximum contact force\({F_{max}}\)and the maximum displacement\({\delta _{max}}\):

When the deformation exceeds a certain threshold\({\delta _r}\), the contact force during the unloading stage can be expressed as:

Therefore, in the elastoplastic contact model, the equation for the normal contact force–displacement throughout the entire collision process is as follows:

When two spheres make contact, a normal contact force is generated along the surface normal, while a tangential force arises in the direction of the tangent. As the two spheres generate tangential displacement\({\delta _s}\)along the contact surface, the corresponding tangential force can be expressed as\({F_s}\). When a tangential displacement increment denoted as\(\Delta {\delta _s}\)occurs, the resulting increment in the tangential contact force\(\Delta {F_s}\)can be expressed as:

In the equation,\({k_s}\)represents the tangential stiffness, which can be determined from the equivalent Poisson’s ratio, normal stiffness, and normal force. The expression for\({k_s}\)is given by17:

\({\upsilon ^*}\)represents the equivalent Poisson’s ratio in the contact model, \({\upsilon ^*}=\frac{{{\upsilon _i}+{\upsilon _j}}}{2}\).

The Mindlin-Deresiewicz contact theory18 is primarily used to describe the distribution of contact stress between two elastic, circular bodies. This theory extends the Hertz contact theory by accounting for the actual elastic deformations within the contact area. Unlike the simple elliptical or circular pressure distribution in Hertz theory, the Mindlin-Deresiewicz model considers the coupled nature of normal and tangential contact forces. Consequently, the incremental superposition method is employed to calculate the tangential contact force, with the expression given by:

Therefore, the tangential contact force generated throughout the entire collision process between the two spheres can be expressed as:

In the equation, \(\mu\)represents the coefficient of sliding friction.

In this study, the control unit stranded wire is composed of multiple copper wires twisted together following a specific manufacturing process. The KA4-type control unit stranded wire (with pitch of 39 mm and a copper wire diameter of 0.39 mm) was peeled and cut into specimens of the same length, which were then conditioned at room temperature for 24 h. The tensile tests were conducted using a universal testing machine. The speed of the tensile testing machine was set to 50 mm/min19 with the load measured by an integrated sensor and recorded by the computer. The specimens were gripped at both ends by the machine’s fixtures, with an initial gauge length of 100 mm20. As the load increased, the outermost copper wires began to fracture, eventually leading to the failure of the majority of the copper wires. The testing machine ceased loading once this occurred (as shown in Fig. 6). At full stability, the data on load and displacement were collected, and the stress-strain curve of the specimen was subsequently generated through further data processing.

Tensile test of the control unit stranded wire: (a) before the test; (b) after the test.

The discrete element model of the control unit stranded wire, established using the method described above, defines that the outer wire has a lay diameter of 1.165 mm, the pitch of 39 mm, and a total length of 120 mm, with a friction coefficient of 0.2 between the copper wires. The deformation characteristics of the stranded wire under axial load were predicted, and the predicted stress-strain curve was compared with the results obtained from the tensile tests described in Sect. 4.1, as shown in Fig. 7. From Fig. 7, it can be observed that the control unit stranded wire undergoes three distinct stages under axial tensile load: In the first stage, the stranded wire undergoes elastic deformation, and the stress-strain relationship is linear. In the second stage, after the stress reaches the yield strength, the wire enters the yield phase and undergoes permanent deformation. In the third stage, when the stress exceeds the tensile strength of the stranded wire, there is a sharp drop in stress, and the stranded wire begins to fracture. During the progressive failure process, the stress increases nonlinearly to a peak before suddenly dropping, but it does not fall to zero, indicating that not all individual wires in the control unit stranded wire have fractured, and some load is still being carried. The fracture elongation and tensile strength measured from the tensile test were 28.57% and 311.01 MPa, respectively. The fracture elongation and tensile strength predicted by the discrete element model were 26.94% and 294.00 MPa, with relative errors of 5.71% and 5.47%, respectively. The discrepancies between the experimental and simulation results may be attributed to several factors, including variations in the friction coefficient between the copper wires in the experiment compared to the DEM, as well as modeling errors during the stranded wire discretization process. Despite these differences, the discrete element predictions closely align with the experimental results, and the stress-strain curves match well. Therefore, the DEM of the control unit stranded wire effectively characterizes and predicts the mechanical response of the stranded wire under load.

Comparison of Stress-strain curves from the DEM simulation and the tensile test.

The pitch of the copper wires inside the control unit stranded wire is one of the key factors affecting its mechanical properties. Based on the production process of the control unit of shearer cables, the pitch of the KA4 control unit stranded wire ranges from 39 mm to 54 mm. Control unit stranded wires with the copper wire diameter of 0.39 mm and the pitch of 39 mm, 44 mm, 49 mm, and 54 mm were modeled, and the wires were discretized according to the method described in Sect. 2.2. The mechanical response of the discretized stranded wire under axial load was predicted, and the resulting stress-strain curves are shown in Fig. 8. As seen in the figure, fracture occurs at the midsection of the stranded wire, with all the outer copper wires breaking, while some of the inner copper wires remain intact (consistent with the tensile test results shown in Fig. 6(b)). It also indicates that, under axial load, the outer copper wires experience higher stress than the inner copper wires.

As shown in Fig. 8, the stranded wire undergoes three distinct stages—elastic, plastic, and fracture—under axial tensile load for all four kinds of pitch. When the copper wire diameter is 0.39 mm and the pitch is 39 mm, 44 mm, 49 mm, and 54 mm, the corresponding tensile strengths are 294.00 MPa, 282.12 MPa, 268.56 MPa, and 266.16 MPa, respectively, and the fracture elongations are 26.94%, 26.24%, 25.84%, and 25.53%. Clearly, the pitch has a significant effect on the stranded wire’s stress-strain curve. As the pitch decreases, both the tensile strength and fracture elongation increase. This can be attributed to the fact that shorter pitch results in tighter wire winding, more pronounced helical characteristics, and improved ductility.

Stress–strain curves of the control unit stranded wire with different kinds of pitch.

To summarize the data obtained from the above simulations, an exponential function was used to fit the discrete points in order to investigate the effect of pitch on the fracture elongation rate and the fracture elongation rate corresponding to any pitch within the range of 39–54 mm. Exponential function fitting is particularly suitable for data exhibiting “growth” or “decay” trends, especially when the data are influenced by a factor whose rate of change is not linear, but instead accelerates or decelerates. For nonlinear relationships, the exponential function is better equipped to capture the changes in the data. The function is expressed as follows21:

A represents the scaling factor of the exponential function; B denotes the rate of exponential growth or decay; and C is the constant term, which indicates the offset of the curve.

The error between the actual data and the model’s predicted values is given by:

Therefore, the sum of squared errors for all data points is given by:

Since the function is nonlinear, the Levenberg-Marquardt algorithm22, which combines gradient descent and Newton’s method, was used to find the optimal parameters of the objective function.

The fracture elongation rate reflects the deformation ability of the wire under external forces and is a key indicator for evaluating the mechanical properties of the stranded wire. To avoid overfitting in the fitting curve between pitch and fracture elongation rate, three additional simulation datasets (for a total of seven datasets) were generated using the discrete element method, as shown in Fig. 9. Leave-One-Out Cross-Validation (LOO-CV) was employed to accurately assess the model’s generalization ability. LOO-CV is particularly useful for small datasets, as it repeatedly trains and validates the model, ensuring that each data point is used as a validation set. This method tests the model’s performance across all data points, preventing overfitting with limited data. Python code was written to divide the dataset into seven samples, using one sample as the validation set while the remaining six samples served as the training set. The prediction error for each iteration was calculated and recorded. This process was repeated until all samples had been used as the validation set. Finally, the average mean squared error (MSE) was computed to evaluate the model’s generalization ability. The resulting fitting curve equation is\(y=62.8958{e^{ - 0.0900x}}+25.0662\), with an average MSE of 0.0018. Therefore, the model demonstrates a good fit without overfitting.

Figure 9 shows the effect of pitch on the fracture elongation rate and its corresponding fitting curve. As shown in Fig. 9, shorter pitch results in higher fracture elongation. The fitted curve can predict the fracture elongation for stranded wire with pitch ranging from 39 mm to 54 mm. When the pitch is 54 mm and 49 mm, the fracture elongation values are similar, and the influence of pitch on the stress-strain curve becomes less pronounced. This is because as the pitch increases, the helical characteristics of the wire weaken, leading to a reduced ductility under axial load. Therefore, in the design process, reducing the pitch can improve the mechanical performance of the stranded wire.

The effect of pitch on fracture elongation rate and its fitted curve.

The impact of the copper wire diameter used in the control unit stranded wire on their mechanical properties has long been a subject of debate. Based on the stranding process of the control unit stranded wire of shearer cables (as shown in Table 1), The KA4 control unit stranded wire is currently constructed from copper wires with diameters of 0.25 mm, 0.3 mm, and 0.39 mm. Using the stranding process and the method described in Sect. 2.2, discrete element models for the three wire specifications with the pitch of 39 mm were developed. Axial load was applied to these models to predict their mechanical response, and the resulting stress-strain curves are shown in Fig. 10. As shown in Fig. 10, when the copper wire diameters are 0.25 mm, 0.30 mm, and 0.39 mm, the corresponding tensile strengths are 263.46 MPa, 272.58 MPa, and 294.00 MPa, respectively, and the fracture elongations are 23.93%, 24.49%, and 26.94%. As the copper wire diameter increases, both the tensile strength and fracture elongation of the wire increase. When the copper wire diameters are 0.25 mm and 0.30 mm, the stress-strain curves of the stranded wire are quite similar. However, when the diameter is 0.39 mm, both the tensile strength and fracture elongation increase significantly. Therefore, increasing the diameter of the copper wire in the stranding can enhance the ductility of the control unit stranded wire of shearer cables.

Stress–strain curves of control unit stranded wire with different copper wire diameters.

To summarize the data obtained from the simulations, an exponential function was used to fit the discrete points in order to study the effect of copper wire diameter on the fracture elongation rate and the fracture elongation rate corresponding to any copper wire diameter within the range of 0.25–0.39 mm. To prevent overfitting in the fitting curve, four additional discrete element simulation data points (for a total of seven datasets) were generated, as shown in Fig. 11. The fitting method described in Sect. 5.1 was applied, and the model’s generalization ability was validated using LOO-CV. Python code was employed to compute the fitting curve, resulting in the following equation\(y=0.0020{e^{18.8726x}}+23.7610\). MSE was 0.0076, indicating that the model provides a good fit without overfitting.

Figure 11 shows the relationship between copper wire diameter and fracture elongation rate, along with the corresponding fitted curve. As observed, the fracture elongation rate increases with the copper wire diameter, and the effect of the diameter on the fracture elongation rate becomes more pronounced as the diameter increases. The fracture elongation rate at a copper wire diameter of 0.39 mm is 12.58% higher than that at 0.25 mm. The fitted curve for the copper wire diameter and fracture elongation rate provides a clear representation of the fracture elongation rate for any copper wire diameter within the range of 0.25 mm to 0.39 mm.

The effect of copper wire diameter on fracture elongation rate and its fitted curve.

This study proposes a modeling approach based on the Discrete Element Method (DEM), which accounts for nonlinear plastic deformation and the complex multi-body contact characteristics induced by twisting. Using this discrete element model, the study analyzes the effects of twist pitch and copper wire diameter on mechanical behavior under axial load. The main conclusions are as follows:

A discrete element model for the control unit stranded wire was developed, and the stress-strain curve under axial load closely matches the corresponding tensile test results, validating the feasibility and accuracy of the discrete element modeling approach.

The stranded wire with four kinds of different twist pitch exhibits three distinct stages under axial tensile load: the elastic stage, plastic stage, and fracture stage. When the copper wire diameter is 0.39 mm and the twist pitch is 39 mm, 44 mm, 49 mm, and 54 mm, the tensile strengths are 294.00 MPa, 282.12 MPa, 268.56 MPa, and 266.16 MPa, respectively, while the fracture elongations are 26.94%, 26.24%, 25.84%, and 25.53%. As the twist pitch decreases, the tensile strength and fracture elongation increase. When the twist pitch is greater than or equal to 49 mm, the effect of twist pitch on the stress-strain curve becomes significantly weaker.

The stress-strain curves of stranded wire with three different diameters show consistent trends under axial tensile load. When the pitch is 39 mm and the copper wire diameters are 0.25 mm, 0.30 mm, and 0.39 mm, the corresponding tensile strengths are 263.46 MPa, 272.58 MPa, and 294.00 MPa, respectively, while the fracture elongations are 23.93%, 24.49%, and 26.94%. As the copper wire diameter increases, both tensile strength and fracture elongation increase. At a diameter of 0.39 mm, the tensile strength and fracture elongation show significant improvements, with the elongation increasing by 12.58% compared to the 0.25 mm diameter, indicating a notable enhancement in ductility.

Authors will provide data upon journal request, If necessary, please contact the corresponding author: Zhongjian Bai，E-mail: [email protected].

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School of Mechanical Engineering, Liaoning Technical University, Fuxin, 123000, China

Lijuan Zhao, Zhongjian Bai & Guocong Lin

Liaoning Provincial Key Laboratory of Large-Scale Mining Equipment, Fuxin, 123000, China

Lijuan Zhao

Shandong Yankuang Group Changlong Cable Manufacture Co., Ltd., Jining, 273522, China

Hongqiang Zhang & Zifeng Liu

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Lijuan Zhao: Investigation, Resources, Writing - Original Draft, Funding acquisition. Zhongjian Bai*: Formal analysis, Investigation, Writing - Original Draft. Hongqiang Zhang: Conceptualization, Supervision, Writing - Review & Editing. Guocong Lin: Methodology, Validation, Resources, Methodology.Zifeng Liu: Validation, Provide experimental equipment.

Correspondence to Zhongjian Bai.

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Zhao, L., Bai, Z., Zhang, H. et al. Research on the discrete element modeling method and tensile fracture behavior of the control unit stranded wire of Shearer cables. Sci Rep 15, 11756 (2025). https://doi.org/10.1038/s41598-025-94961-8

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Received: 11 November 2024

Accepted: 18 March 2025

Published: 06 April 2025

DOI: https://doi.org/10.1038/s41598-025-94961-8

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