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三维颗粒体系颗粒间接触力计算是散体力学研究的重难点. 以双弹性橡胶球为研究对象, 开展显微CT (micro-CT)原位平压实验, 基于Hertz接触理论和Tatara大变形接触理论, 验证了弹性球接触模型, 获得了基于实验的弹性球接触力理论公式. 以三维颗粒体系为研究对象, 开展了micro-CT原位探针加载实验, 获取颗粒二维图像序列, 经过系列数字变换得到数字体图像, 获得了不同加载状态下三维颗粒体系接触力网络, 分析了颗粒体系接触力分布及演化规律, 探究了强接触数量及分布演化与颗粒体系稳定性的联系. 研究结果表明: 基于实验的弹性球接触力公式能合理有效表征两颗粒间的接触力; 探针加载下颗粒间接触力呈现以探针压头接触点为起点, 向下方和四周逐级传递接触力的网状分布; 强接触数量占接触总数量的45%—50%, 分布贯穿于整个颗粒体系内部, 支撑起颗粒体系网络结构, 较大值集中于压头下方呈现树杈状分布; 加载过程中, z = 14 mm处建立了平衡点, 平衡点处, 强接触数量达到顶峰, 强接触力网络结构布满整个三维颗粒体系, 建立起承受外载荷的主要骨架, 随着加载继续, 强接触力的整体数值更高, 在颗粒体系内部分布也更加均匀.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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图 2 单球颗粒法向重叠量$ \delta $与接触力F关系
Fig. 2. Relationship between normal overlap $ \delta $ and contact force F for single granule.
图 10 应变$ \varepsilon $-接触力F关系
Fig. 10. Relationship of strain $ \varepsilon $ and contact force F.
图 11 应变$ \varepsilon $-接触面积A关系
Fig. 11. Relationship of strain $ \varepsilon $ and contact area A.
图 14 接触力网络分布及演化计算流程图
Fig. 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
Fig. 15. Contact force network distribution and evolution of granular systems.
图 17 接触总数量NT和平均接触力$ \overline F $变化
Fig. 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
Fig. 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
Fig. 19. Strong contact force network distribution and evolution more than 10.78 N of granular systems.
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[1] 孙其诚 2015 物理学报 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 物理学报 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 物理学报 57 4667
Google Scholar
Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667
Google Scholar
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Google Scholar
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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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