An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method
Abstract
:1. Introduction
2. Experimental Method
2.1. Design and Properties of Specimens
2.2. Experimental Equipment
2.3. Experimental Procedure
- (1)
- The upper specimen was struck by controlling the angle of the impact force hammer, and the force was transmitted to the contact surface between the specimens through the compression caused by the impact.
- (2)
- When impacted, the pressure sensor on the impact force hammer generated a charge signal, which was converted into a voltage signal by the signal converter. The thin-film pressure sensor generated a corresponding current signal when sensing pressure, which was converted into a voltage signal by a linear voltage conversion module. The strain gauge changed its resistance due to deformation, and the signal amplifier converted it into a voltage signal. These three sets of signals were transmitted to the dynamic signal acquisition instrument.
- (3)
- The dynamic signal acquisition instrument transmitted the data to the dynamic signal testing and analysis software on the PC through a network cable, and generated data waveforms collected by the force hammer pressure sensor, thin-film pressure sensor, and strain gauge, thereby obtaining the time–domain curve of the impact force of the force hammer, the contact force between the blocks, and the strain curve.
2.4. Magnitude of Impact Force
3. Calculation of Contact Force
3.1. Contact Depth
3.2. Normal Stiffness
3.3. Stiffness Correction Factor
4. Comparison between DEM and Experimental Results
4.1. Two Elements under Edge–Edge Contact Mode
4.1.1. Collinear
4.1.2. Non-Collinear
4.2. Two Elements under Point–Edge Contact Mode
4.3. Two Elements under Point–Face Contact Mode
4.4. Two Elements under Edge–Face Contact Mode
4.5. Two Elements under Face–Face Contact Mode
5. Verification of Simulation
5.1. Packing Experiment of Multiple Cubes
5.2. Comparison between Packing Experiment and Simulation
5.2.1. Cubes with an Edge Length of 20 mm
5.2.2. Cubes with an Edge Length of 25 mm
5.2.3. Cubes with an Edge Length of 30 mm
5.3. Packing Simulation of Randomly Shaped Polyhedral Elements
6. Conclusions
- The experimental method designed in this study can be employed to test the contact forces between polyhedral blocks under different modes. A contact stiffness correction coefficient was introduced into the Cundall model, leading to the construction of an improved contact force model suitable for polyhedral elements.
- The improved contact force model was incorporated into the DEM. An analysis of simulated contact force peaks and force patterns revealed an improved accuracy of the model, and this would affect the motion behavior of polyhedral elements.
- The DEM simulation methods, both before and after the improvement, were applied to packing experiments with cubic specimens. A comparative analysis of the results confirmed the improved accuracy and reliability of the improved contact force model in simulating the contact of polyhedral elements.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Group | Edge–Edge (Collinear) | Point–Edge | Point–Face | Edge–Edge (Non-Collinear) | Edge–Face | Face–Face |
---|---|---|---|---|---|---|
1 | 65.31 | 68.60 | 69.84 | 69.10 | 80.42 | 62.81 |
2 | 72.28 | 70.14 | 71.26 | 70.35 | 83.64 | 68.11 |
3 | 78.18 | 73.53 | 74.20 | 72.49 | 87.37 | 73.58 |
4 | 111.14 | 114.52 | 117.18 | 115.49 | 115.21 | 120.73 |
5 | 115.79 | 118.85 | 121.55 | 118.68 | 118.96 | 124.65 |
6 | 121.82 | 125.21 | 122.59 | 123.01 | 123.51 | 127.09 |
7 | 176.68 | 165.72 | 165.82 | 149.46 | 166.90 | 172.87 |
8 | 177.35 | 169.34 | 168.69 | 155.23 | 170.21 | 173.62 |
9 | 179.68 | 175.09 | 173.92 | 160.57 | 174.86 | 176.82 |
Group | Edge–Edge (Collinear) | Point–Edge | Point–Face | Edge–Edge (Non-Collinear) | Edge–Face | Face–Face |
---|---|---|---|---|---|---|
1 | −9.1 × 10−8 | −8.4 × 10−8 | −6.1 × 10−8 | −6.9 × 10−8 | −8.6 × 10−8 | −7.2 × 10−8 |
2 | −9.1 × 10−8 | −7 × 10−8 | −5.9 × 10−8 | −7.3 × 10−8 | −1 × 10−7 | −7 × 10−8 |
3 | −1 × 10−7 | −9 × 10−8 | −8.5 × 10−8 | −6.7 × 10−8 | −7.8 × 10−8 | −7.8 × 10−8 |
4 | −1.4 × 10−7 | −9.7 × 10−8 | −9.8 × 10−8 | −9.6 × 10−8 | −1.1 × 10−7 | −1.4 × 10−7 |
5 | −1.4 × 10−7 | −1.1 × 10−7 | −1.2 × 10−7 | −8.2 × 10−8 | −1 × 10−7 | −1.2 × 10−7 |
6 | −1.3 × 10−7 | −1.2 × 10−7 | −1.2 × 10−7 | −1.1 × 10−7 | −1.2 × 10−7 | −1.2 × 10−7 |
7 | −2 × 10−7 | −1.5 × 10−7 | −2.2 × 10−7 | −1.4 × 10−7 | −1.4 × 10−7 | −1.4 × 10−7 |
8 | −2.1 × 10−7 | −1.4 × 10−7 | −2 × 10−7 | −1.2 × 10−7 | −1.9 × 10−7 | −1.8 × 10−7 |
9 | −2.1 × 10−7 | −1.6 × 10−7 | −2.5 × 10−7 | −1.5 × 10−7 | −1.8 × 10−7 | −1.8 × 10−7 |
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Wang, Y.; Liu, J.; Zhen, M.; Liu, Z.; Zheng, H.; Zhao, F.; Ou, C.; Liu, P. An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method. Appl. Sci. 2024, 14, 311. https://doi.org/10.3390/app14010311
Wang Y, Liu J, Zhen M, Liu Z, Zheng H, Zhao F, Ou C, Liu P. An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method. Applied Sciences. 2024; 14(1):311. https://doi.org/10.3390/app14010311
Chicago/Turabian StyleWang, Yue, Jun Liu, Mengyang Zhen, Zheng Liu, Haowen Zheng, Futian Zhao, Chen Ou, and Pengcheng Liu. 2024. "An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method" Applied Sciences 14, no. 1: 311. https://doi.org/10.3390/app14010311
APA StyleWang, Y., Liu, J., Zhen, M., Liu, Z., Zheng, H., Zhao, F., Ou, C., & Liu, P. (2024). An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method. Applied Sciences, 14(1), 311. https://doi.org/10.3390/app14010311