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The calculation of inter-granule contact force in three-dimensional (3D) granular systems is a key and challenging aspect of granular mechanics research. Two elastic rubber balls are used as research objects for in-situ flat pressing micro-CT experiments. Based on the Hertzian contact theory and Tatara large deformation contact theory, the contact model of elastic balls is verified, and the theoretical formula of the contact force of elastic balls based on the experiment is obtained. Taking the 3D granular systems as research object, in-situ probe loading experiment of micro-CT is carried out to obtain the 2D image sequence of the granules, after a series of digital transformations, the digital body images emerge, the contact force networks of the 3D granular systems under different loading conditions are obtained by constructing pore network models. The contact force distribution and evolution law of the granular systems are analyzed. The relation among the number of strong contacts, the distribution evolution, and the stability of the granular system is explored. The results show that the two elastic ball contact model conforms to the Hertzian contact theory and Tatara large deformation contact theory, and the contact force fitting formula based on experiment can characterize the contact force between two granules reasonably and effectively. The contact force of granules under probe loading is distributed in a net-like pattern starting from the contact point of the indenter and gradually transmitted to the lower and the surrounding area. The trend of average contact force is consistent with the trend of the contact times, showing a significant phase transition. With the increase of contact times, the frequency of particle compression increases, resulting in a greater contact force between granules, ultimately stabilizing at about 10.5 N. The number of strong contacts accounts for 45% to 50% of the total number of contacts, distributed throughout the whole granular system and supporting the network structure of the granular system. The larger values are concentrated below the indenter and exhibit a branching distribution. In the loading process, an equilibrium point is established at z = 14 mm, where the number of strong contacts reaches the peak. The network structure of strong contact force is spread throughout the entire 3D granular system, establishing the main skeleton that can withstand external loads. As the loading continues, the total value of strong contact forces increases, and their distribution within the granular system becomes more uniform.
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Keywords:
- micro-CT /
- in-situ loading /
- contact model of granules /
- contact force
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Google Scholar
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图 1 Hertz接触模型
Figure 1. Hertz contact model.
图 2 单球颗粒法向重叠量$ \delta $与接触力F关系
Figure 2. Relationship between normal overlap $ \delta $ and contact force F for single granule.
图 3 Micro-CT系统
Figure 3. Micro-CT system.
图 4 实验模型
Figure 4. Test model.
图 5 压头和试样
Figure 5. Indenter and specimen.
图 6 图像处理流程
Figure 6. Image processing flow.
图 7 双弹性颗粒实验模型
Figure 7. Experimental model of two granules.
图 8 压头和试样
Figure 8. Indenter and specimen.
图 9 双颗粒不同速度z-P曲线
Figure 9. The z-P curves for two granules with different velocities.
图 10 应变$ \varepsilon $-接触力F关系
Figure 10. Relationship of strain $ \varepsilon $ and contact force F.
图 11 应变$ \varepsilon $-接触面积A关系
Figure 11. Relationship of strain $ \varepsilon $ and contact area A.
图 12 接触面积A-接触力F关系
Figure 12. Relationship of contact area A and contact force F.
图 13 颗粒体系受压情况
Figure 13. Granular systems pressure situation.
图 14 接触力网络分布及演化计算流程图
Figure 14. Flowchart for calculation of contact force network distribution and evolution.
图 15 颗粒体系接触力网络分布及演化
Figure 15. Contact force network distribution and evolution of granular systems.
图 16 接触力区间变化
Figure 16. Change in contact force interval.
图 17 接触总数量NT和平均接触力$ \overline F $变化
Figure 17. Change in total number of contacts NT and average contact force $ \overline F $.
图 18 颗粒体系强接触力网络分布及演化
Figure 18. Strong contact force network distribution and evolution of granular systems.
图 19 颗粒体系高于10.78 N的强接触力网络分布及演化
Figure 19. Strong contact force network distribution and evolution more than 10.78 N of granular systems.
图 20 强接触数量NS变化
Figure 20. Change in number of strong contacts NS.
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[1] 孙其诚 2015 64 076101
Google Scholar
Sun Q C 2015 Acta Phys. Sin. 64 076101
Google Scholar
[2] 瞿同明, 冯云田, 王孟琦, 赵婷婷, 狄少丞 2021 力学学报 53 2404
Google Scholar
Qu T M, Feng Y T, Wang M Q, Zhao T T, Di S C 2021 Chin. J. Theor. Appl. Mech. 53 2404
Google Scholar
[3] Wang Y W, Liu R, Sun R H, Xu Z W 2023 Eng. Comput. 40 1390
Google Scholar
[4] Lovoll G, Måloy K J, Flekkoy E G 1999 Phys. Rev. E 60 5872
Google Scholar
[5] Blair D L, Mueggenburg N W, Marshall A H, Jaeger H M, Nagel S R 2000 Phys. Rev. E 63 278
Google Scholar
[6] Anton K, Neverov S, Neverov A, Dmitry O, Ivan Z, Maria K 2023 Geohazard Mech. 1 128
Google Scholar
[7] 鲁锋, 李照阳, 杨召, 张刘平, 刘金, 李璐璐, 刘向军 2023 石油实验地质 45 193
Google Scholar
Lu F, Li Z Y, Yang Z, Zhang L P, Liu J, Li L L, Liu X J 2023 Pet. Geol. Exp. 45 193
Google Scholar
[8] Wang S T, Chang Y H, Wang Z F, Su X X 2024 Energies 17 1370
Google Scholar
[9] Majmudar T S, Behringer R P 2005 Nature 435 1079
Google Scholar
[10] Sanfratello L, Fukushima E, Behringer R P 2009 Granular Matter 11 1
Google Scholar
[11] 陈凡秀, 庄琦, 王日龙 2016 岩土力学 37 563
Google Scholar
Chen F X, Zhuang Q, Wang R L 2016 Rock Soil Mech. 37 563
Google Scholar
[12] Kondo A, Takano D, Kohama E, Bathurst R J 2022 Géotech. Lett. 12 203
[13] 王潇, 陈凡秀, 王远, 刘雨欣, 孙洁 2023 力学学报 55 1732
Wang X, Chen F X, Wang Y, Liu Y X, Sun J 2023 Chin. J. Theor. Appl. Mech. 55 1732
[14] Hertz H 1881 J. Reine Angew. Math. 92 156
Google Scholar
[15] Johnson K L, Kendall K, Roberts A D 1971 Proc. R. Soc. London, Ser. A 324 301
Google Scholar
[16] Derjaguin B V, Muller V M, Toporov Y P 1975 J. Colloid Interface Sci. 53 314
Google Scholar
[17] Tatara Y 1991 ASME J. Eng. Mater. Technol. 113 285
Google Scholar
[18] Tatara Y, Shima S, Lucero J C 1991 ASME J. Eng. Mater. Technol. 113 292
Google Scholar
[19] 何思明, 吴永, 李新坡 2008 工程力学 25 19
He S M, Wu Y, Li X P 2008 Eng. Mech. 25 19
[20] 运睿德, 丁北 2019 机械工程学报 55 80
Yun R D, Ding B 2019 J. Mech. Eng. 55 80
[21] Wu Y, Hao H C, Gao M Z, Gao Z, Gao Y N 2023 Geomech. Geophys. Geo-Energy Geo-Resour. 9 126
Google Scholar
[22] 戚俊成, 陈荣昌, 刘宾, 陈平, 杜国浩, 肖体乔 2017 66 054202
Google Scholar
Qi J C, Chen R C, Liu B, Chen P, Du G H, Xiao T Q 2017 Acta Phys. Sin. 66 054202
Google Scholar
[23] Lubner M G, Ziemlewicz T J, Wells S A, Li Ke, Wu P H, Hinshaw J L, Lee F T, Brace C L 2022 Abdominal Radiology 47 2658
Google Scholar
[24] Busch M, Hausotte T 2022 Prod. Eng. 16 411
Google Scholar
[25] 毛灵涛, 毕玉洁, 刘海洲, 陈俊, 王建强, 彭瑞东, 刘红彬, 吴昊, 孙跃, 鞠杨 2023 科学通报 68 380
Google Scholar
Mao L T, Bi Y J, Liu H Z, Chen J, Wang J Q, Peng R D, Liu H B, Wu H, Sun Y, Ju Y 2023 Chin. Sci. Bill. 68 380
Google Scholar
[26] Sakamoto S, Suzuki K, Toda K, Seino S 2022 Materials 15 7393
Google Scholar
[27] Zhuang C, Jianfeng W, Wei X 2023 Géotech. 21 1
Google Scholar
[28] 孙其诚, 王光谦 2008 57 4667
Google Scholar
Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667
Google Scholar
[29] Pérez L G, Bernal P L J, Alés F V, del-Río J J M, Borreguero M, Ochoa J M A 2024 Boletín de la Sociedad Españ ola de Cerámicay Vidrio 63 216
[30] Wu Z H, Yang Y H, Zuo Y J, Meng X R, Wang W T, Lei W L 2023 Acta Geophys. 72 2503
Google Scholar
[31] Fang H, He N 2023 Appl. Sci. 13 12270
Google Scholar
[32] 雷健, 潘保芝, 张丽华 2018 地球物理学进展 33 653
Google Scholar
Lei J, Pan B Z, Zhang L H 2018 Prog. Geophys. 33 653
Google Scholar
[33] Hosseinzadegan A, Raoof A, Mahdiyar H, Nikooee E, Ghaedi M, Qajar J 2023 Geoenergy Sci. Eng. 226 211
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