基于应力波动的修正非局部流变模型

叶晓燕; 王等明; 郑晓静

doi:10.6052/0459-1879-15-287

基于应力波动的修正非局部流变模型

1.
兰州大学西部灾害与环境力学教育部重点实验室, 土木工程与力学学院, 兰州 730000
2. 西安电子科技大学机电工程学院, 西安 710071

基金项目: 国家科技支撑项目(2013BAC07B01),国家自然科学基金(11421062,11572144,11502104,11072097),兰州大学中央高校基本科研业务费专项基金(lzujbky-2015-177),国家教育部科学基金(308022),中国博士后基金(2013M530434)和兰州大学西部灾害与环境力学教育部重点实验室开放基金(201404)资助项目.

详细信息

通讯作者:
王等明,博士,副教授,研究方向:颗粒介质力学.E-mail:dmwang@lzu.edu.cn

中图分类号: O371
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出版历程
- 收稿日期: 2015-07-29
- 修回日期: 2015-08-04
- 刊出日期: 2016-01-17

A MODIFIED NONLOCAL RHEOLOGY MODEL FOR DENSE GRANULAR FLOW

1.
Key Laboratory of Mechanics on Environment and Disaster in Western China, The Ministry of Education of China, Department of Mechanics and Engineering Sciences, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
2. School of Electronical and Machanical Engineering, Xidian University, Xi'an 710071, China

摘要

摘要: 基于Pouliquen 提出的非局部流变模型,考虑颗粒流中某个位置重新排列引起的自激发过程,详细分析颗粒介质中应力波动幅值的概率密度分布形式以及剪切速率与体积分数的耦合作用,提出一种修正的非局部流变模型. 采用此修正非局部流变模型对斜面剪切颗粒流的流动特性进行了预测,颗粒流动的临界厚度、平均流动速度及剪切速率廓线的预测结果与实验结果定量吻合. 此修正模型的提出为复杂的密集颗粒流的描述和表征提供了一种新的研究思路.
- 应力波动 /
- 修正的非局部流变模型 /
- 体积分数 /
- 概率密度分布
Abstract: In dense granular flows, a non-local rheology theory was proposed by Pouliquen et al. based on the idea of a self-activated process, in which a rearrangement at one position will be trigged by stress fluctuation due to rearrangements elsewhere in the material. Taking into account the probability density distribution of stress fluctuation amplitude in granular materials and the coupling e ect between shear rate and volume fraction in iterative calculation, a modified non-local rheological model was proposed in order to describe the dense granular flow more accurately. Due that dense granular flows down inclines preserve this complexity but remain simple enough for detailed analysis, this modified model was applied to predict the rheological characteristics of flows down a rough inclined plane. Compared to the previous non-local rheological model, the predicted results based on the present modified model, including the critical thickness, depth-averaged velocity and shear rate profile, are quantitatively better consistent with the existing experimental and simulating results.
- stress fluctuation /
- modified non-local rheological model /
- volume fraction /
- probability density distribution

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参考文献(40)

1 Zheng XJ, Wang DM. Multiscale mechanical behaviors in discrete materials: A review. Acta Mechanica Solida Sinica, 2010, 23(6):579-591

2 Pouliquen O, Chevoir F. Dense flows of dry granular material. C. R. Physique, 2002, 3: 163-175

3 季顺迎. 非均匀颗粒材料的类固-液相变行为及本构方程. 力学学报, 2007, 23(2): 223-237 (Ji Shunying. The quasi-solid-liquid phase transition of non-uniform granular materials and their constitutive equation. Chinese Journal of Theoretical and Applied Mechanics,2007, 23(2): 223-237 (in Chinese))

4 Aranson IS, Tsimring LS. Patterns and collective behavior in granular media: Theoretical concepts. Rev Mod Phys, 2006, 78: 641-692

5 蒋亦民, 刘佑. 基于流体动力学理论的颗粒物质本构关系. 科学通报, 2009, 54(11): 1504-1510 (Jiang Yimin, Liu Mario. A granular constitutive relation derived from hydrodynamics. Chinese Sci Bull, 2009, 54(11): 1504-1510 (in Chinese))

6 季顺迎, 孙其诚, 严颖. 颗粒物质剪切流动的类固-液转化特性及相变图的建立. 中国科学物理学力学天文学(中文版), 2011,41(9): 1112-1125 (Ji Shunying, Sun Qicheng, Yan Ying. Characteristics in quasi-solid-liquid phase transition of granular shear flow and its phase diagram. Sci. Sin. Phys. Mech. Astron, 2011, 41(9):1112-1125 (in Chinese))

7 Jaeger HM, Nagel SR, Behringer RP. Granular solids, liquids, and gases. Rev Mod Phys, 1996, 68: 1259-1273

8 Roux JN, Combes G. Quasistatic rheology and the origin of strain. C R Phys, 2002, 3: 131-140

9 Goldhirsch I. Rapid granular flows. Annu Rev Fluid Mech, 2003, 35:267-293

10 Berzi D. Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mech, 2014, 225: 2191-2198

11 Midi GDR. On dense granular flows. Eur Phys J E, 2004, 14: 341-365

12 Da Cruz F, Emam S, Prochnow M, et al. Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys Rev E, 2005, 72: 021309

13 Bagnold RG. Experiments of gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond A, 1954,255: 49-63

14 Jop P, Forterre Y, Pouliquen O. A constitutive law for dense granular flows. Nature, 2006, 441: 727-730

15 Silbert LE, Landry JW, Grest GS. Granular flow down a rough inclined plane: Transition between thin and thick piles. Phys Fluids,2003, 15: 1-10

16 Mueth DM, Debregeas GF, Karczmar GS, et al. Signatures of granular microstructure in dense shear flows. Nature, 2000, 406: 385-389

17 Koval G, Roux JN, Corfdir A, et al. Annular shear of cohesionless granularmaterials: From the inertial to quasistatic regime. Phys Rev E, 2009, 79: 021306

18 Kamrin K, Koval G. Nonlocal constitutive relation for steady granular flow. Phys Rev Lett, 2012, 108: 178301

19 Aranson IS, Tsimring LS. Continuum theory of partially fluidized granular flows. Phys Rev E, 2002, 65: 061303

20 Mohan LS, Rao KK, Nott PR. A frictional cosserat model for the slow shearing of granular materials. J Fluid Mech, 2002, 457: 377-409

21 Savage SB. Analysis of slow high-concentration flows of granular materials. J Fluid Mech, 1998, 377: 1-26

22 Jenkins JT, Berzi D. Dense inclined flows of inelastic spheres: Tests of an extension of kinetic theory. Granular Matter, 2010, 12: 151-158

23 Kamrin K, Bazant MZ. Stochastic flow rule for granular materials. Phys Rev E, 2007, 75: 041301

24 Jop P. Rheological properties of dense granular flows. C R Physique,2015, 16: 62-72

25 Bouzid M, Trulsson M, Claudin P, et al. Microrheology to probe non-local e ects in dense granular flows. Eur Phy Lett, 2015, 109:24002

26 Henann DL, Kamrin K. A predictive, size-dependent continuum model for dense granular flows. Proceedings of the National Academy of Sciences, 2013, 110: 6730

27 Kamrin K, Henann DL. Nonlocal modeling of granular flows down Inclines. Soft Matter, 2015, 11: 179-185

28 Pouliquen O, Forterre Y. A non-local rheology for dense granular flows. Philos Transact A Math Phys Eng Sci, 2009, 367: 5091-5107

29 Pouliquen O, Forterre Y, Le Dizes S. Slow dense granular flows as self-induced process. Adv Complex Syst, 2001, 4: 441-450

30 Pouliquen O. Scaling laws in granular ows down rough inclined planes. Phys Fluids, 1999, 11: 542-548

31 Müller MK, Luding S, Pöschel T. Force statistics and correlations in dense granular packings. Chemical Physics, 2010, 375: 600-605

32 Coppersmith SN, Liu C, Majumdar S, et al. Model for force fluctuations in bead packs. Phys Rev E, 1996, 53 (5): 4673-4685

33 Liu C, Nagel SR, Schecter DA, et al. Force fluctuations in bead packs. Science, 1995, 269: 513-515

34 Asmus SMF, Pezzotti G. Analysis of microstresses in cement paste by fluorescence piezospectroscopy. Phys Rev E, 2002, 66: 052301

35 Haw MD. Volume fraction variations and dilation in colloids and Granular. Phil Trans R Soc A, 2009, 367: 5167-5170

36 Haw MD. Void structure and cage fluctuations in simulations of concentrated suspensions. Soft Matter, 2006, 2: 950-956

37 Møller PCF, Rodts S, Michels MAJ, et al. Shear banding and yield stress in soft glassy materials. Phys Rev E, 2008, 77: 041507

38 Pusey PN, Zaccarelli E, Valeriani C, et al. Hard spheres: crystallization and glass formation. Phil Trans R Soc A, 2009, 367: 4993-5011

39 Pouliquen O, Cassar C, Jop P, et al. Flow of dense granular material: Towards simple constitutive laws. J Stat Mech, 2006, (07): P07020

40 Silbert LE, Ertas D, Grest GS, et al. Granular flow down inclined plane: Bagnold scaling and rheology. Phys Rev E, 2001, 64: 051302

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基于应力波动的修正非局部流变模型

通讯作者:
王等明,博士,副教授,研究方向:颗粒介质力学.E-mail:dmwang@lzu.edu.cn

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A MODIFIED NONLOCAL RHEOLOGY MODEL FOR DENSE GRANULAR FLOW

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基于应力波动的修正非局部流变模型

通讯作者: 王等明,博士,副教授,研究方向:颗粒介质力学.E-mail:dmwang@lzu.edu.cn

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A MODIFIED NONLOCAL RHEOLOGY MODEL FOR DENSE GRANULAR FLOW

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出版历程

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通讯作者:
王等明,博士,副教授,研究方向:颗粒介质力学.E-mail:dmwang@lzu.edu.cn