-
摘要: 密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统（ADS嬗变）的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.Abstract: A dense granular material (GM) is composed of dense random packing of solid particles and posses disorder structures which has been a long-standing mystery. On the one hand, GMs are amorphous materials with no long-range structural order; on the other hand, both topological and mechanical short range order are pronounced in these materials, due to their high granular packing density. The unique internal structure of GMs underlies their unique mechanical ad physical properties, which render GMs are useful for various applications in more and more engineering and industries in recent years, such as rock-filled dams, granular type debris flows, and the pebble-bed High Temperature Reactor. However, fundamental knowledge on the structural aspect of GMs remains seriously lacking. For example, how the granular mesoscopic structures are formed on the short-to-medium range, how the structure differs in different GMs and changes with granular composition, external loadings, and processing history and methods, and more importantly, how the structure influences the properties of GMS, are still well answered questions. Granular materials are currently the most actively studied materials. In this paper, we review the tremendous efforts over the past decades devoted to unraveling the particle-level structure of GMs and the structural origin of their unique mechanical behaviors, including the simplified inter-particle contact models and the structure measurement techniques and analysis methods. The failure of granular materials play a vital role in transition from solid-to fluid-like states. The related jamming transition, the concepts of"soft spots"and the micro-displacement measurement techniques are then analyzed. Outstanding questions in this research area will be outlined. Suggestions are proposed as well. The studies on the fundamental problems of granular materials should employ the cutting edge studies of the condensed physics and mathematics to establish new concepts. Because of extensive uses in engineering and industries, the fundamental studies are suggested to closely connect with engineering and industries by focusing on the core technologies, which would greatly prompt the development of this research area.
-
Key words:
- granular materials /
- constitutive relations /
- multiple-scale structures /
- contact laws
-
图 2 美国Duke大学开展的颗粒光弹实验采用高速相机观测到了力链结构的演化过程(Clark et al.2015)
图 6 不同压强下的波速. 实验测量结果(Domenico 1977,Makse et al.2004)与基于式(31)的计算结果对比
图 11 有摩擦颗粒体系的Jamming相图(Ciamarra et al.2011)
图 14 软点与颗粒重排图(深色点是软点插图箭头显示了颗粒非仿射位移)(Dong et al.2015)
图 15 (a)塑性事件发生后归一化的非仿射位移图,(b)塑性事件发生前最低频率模式的极化矢量图,(c)投影系数α2随模式数的变化(这些本征模式由发生颗粒重排之前的体系计算而得,颗粒重排矢量为颗粒重排前后的位移)(插图: 投影系数的积累通过计算低于模式数的贡献总和而得(Dong et al.2015)
图 16 (a)散斑能见度光谱技术测量转筒中颗粒的脉动速度装置和(b)脉动速度二阶矩的空间分布(亦即颗粒温度)(Li et al.2016)
表 1 颗粒接触力测量技术汇总
表 2 颗粒速度测量技术汇总
-
冯旭, 张国华, 孙其诚. 2013. 颗粒尺寸分散度对颗粒体系力学和几何结构特性的影响. 物理学报, 62:184501 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201318042.htmFeng X, Zhang G H, Sun Q C. 2013. Effects of size polydispersity on mechanical and geometrical properties of granular system. Acta Physica Sinica, 62: 184501 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201318042.htm 黄文熙. 1983. 土的工程性质. 北京: 水利电力出版社Huang W X. 1983. Engineering Properties of Soil. Beijing: China Water & Power Press 李广信. 2006. 土的清华弹塑模型及其发展. 岩土工程学报, 28: 1-10 http://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200601000.htmLi G X. 2006. Characteristics and development of Tsinghua elasto-plastic model for soil. Chinese Journal of Geotechnical Engineering, 28:1-10 http://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200601000.htm 李家春. 2014. 中国学科发展战略: 流体动力学. 北京: 科学出版社Li J C. 2014. Development Strategy of China Discipline: Fluid Dynamics. Beijing: Science Press 沈珠江. 2000. 理论土力学. 北京: 中国水利水电出版社Shen J Z. 2000. Theoretical Soil Mechanics. Beijing: China Water & Power Press 孙其诚, 厚美瑛, 金峰等. 2011. 颗粒物质物理与力学. 北京: 科学出版社Sun Q C, Hou M Y, Jin F, et al. 2011. Physics and Mechanics of Granular Materials. Beijing: Science Press 孙其诚, 王光谦. 2009. 颗粒介质力学导论. 北京: 科学出版社Sun Q C, Wang G Q. 2009. Introduction to Granular Mechanics. Beijing: Science Press 孙其诚, 王光谦. 2008. 颗粒流动力学及其离散模型评述. 力学进展, 38: 87-100 http://lxjz.cstam.org.cn/CN/abstract/abstract132944.shtmlSun Q C, Wang G Q. 2008. Review on granular flow dynamics and its discrete element method. Advances In Mechanics, 38:87-100 http://lxjz.cstam.org.cn/CN/abstract/abstract132944.shtml 汪卫华. 2013. 非晶态物质的本质和特性. 物理学进展, 33: 177-351 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXJ201305001.htmWang W H. 2013. The nature and properties of amorphous matter. Progress in Physics, 33: 177-351 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXJ201305001.htm 张攀, 赵雪丹, 张国华等. 2016. 垂直载荷下颗粒物质的声波探测和非线性响应. 物理学报, 65: 024501 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201602027.htmZhang P, Zhao X D, Zhang G H, et al. 2016. Acoustic detection and nonlinear response of granular materials under vertical vibrations. Acta Physica Sinica, 65: 024501 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201602027.htm Ai J, Chen J F, Rotter J R, Ooi J Y. 2011. Assessment of rolling resistance models in discrete element simulations. Powder Technology, 206: 269-282 doi: 10.1016/j.powtec.2010.09.030 Aoki K M, Akiyama T. 1995. Simulation studies of pressure and density wave propagations in vertically vibrated beds of granules. Physical Review E, 52: 3288-3291 doi: 10.1103/PhysRevE.52.3288 Basu A, Xu Y, Still T, Arratia P E, Zhang Z, Nordstrom K N, Rieser J M, Gollub J P, Durian D J, Yodh A G. 2014. Rheology of soft colloids across the onset of rigidity: scaling behavior, thermal, and non-thermal responses. Soft Matter, 10: 3027-3035 doi: 10.1039/c3sm52454j Bandyopadhyay R, Gittings A S, Suh S S, Dixon P K, Durian D J. 2005. Speckle-visibility spectroscopy: a tool to study time-varying dynamics. Review of Scientific Instruments, 76: 093110 doi: 10.1063/1.2037987 Bardet J P, Huang Q. Rotational stiffness of cylindrical particle contacts//Proceedings of the Second In-ternational Conference on Micromechanics of Granular Media, Birmingham, UK. Thornton C ed., A. A. Balkema: 39-44. Baxter J, Tüzün U, Burnell J, Heyes D M. 1997. Granular dynamics simulation of two-dimensional heap formation. Physical Review E, 55: 3546-3554 doi: 10.1103/PhysRevE.55.3546 Bi D, Zhang J, Chakraborty B, Behringer R P. 2011. Jamming by shear. Nature, 480: 355-358 doi: 10.1038/nature10667 Brilliantov N V, Spahn F, Hertzsch J, Poeschel T. 1996. Model for collisions in granular gases. Physical Review E, 53: 5382-5392 doi: 10.1103/PhysRevE.53.5382 Brunet T, Jia X, Johnson P A. 2008. Transitional nonlinear elastic behaviour in dense granular media. Geophysical Research Letters, 35: L19308 doi: 10.1029/2008GL035264 Chai L, Wu X, Liu C S. 2014. A universal scaling law of grain chain elasticity under pressure revealed by a simple force vibration method. Soft Matter, 10: 6614-6618 doi: 10.1039/C4SM00727A Chen K, ManningML, Yunker P J, EllenbroekWG, Zhang Z, Liu A J, Yodh A G. 2011. Measurement of cor-relations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses. Physical Review Letters, 107: 108301 doi: 10.1103/PhysRevLett.107.108301 Cheng Y Q, Ma E. 2011. Atomic-level structure and structure-property relationship in metallic glasses. Progress in Materials Science, 56: 379-473 doi: 10.1016/j.pmatsci.2010.12.002 Chou H T, Lee C F. 2009. Cross-sectional and axial flow characteristics of dry granular material in rotating drums. Granular Matter, 11: 13-32 doi: 10.1007/s10035-008-0118-y Ciamarra M P, Pastore R, Nicodemi M, Coniglio A. 2011. Jamming phase diagram for frictional particles. Physical Review E, 84: 041308 doi: 10.1103/PhysRevE.84.041308 Chialvo S, Sun J, Sundaresan S. 2012. Bridging the rheology of granular flows in three regimes. Physical Review E, 85: 0121305 doi: 10.1103/PhysRevB.85.121305 Clark A H, Petersen A J, Kondic L, Behringer R P. 2015. Nonlinear force propagation during granular impact. Physical Review Letters, 114: 144502 doi: 10.1103/PhysRevLett.114.144502 Cooke M H, Bridgwater J. 1982. The simulation of a particle disperse. Powder Technology, 33: 239-247 doi: 10.1016/0032-5910(82)85062-6 Cubuk E D, Schoenholz S S, Rieser J M, Malone B D, Rottler J, Durian D J, Kaxiras E, Liu A J. 2015. Identifying structural flow defects in disordered solids using machine-learning methods. Physical Review Letters, 114: 108001 doi: 10.1103/PhysRevLett.114.108001 Cundall P A. 1971. A Computer model for simulating progressive large scale movements in blocky rock systems//Proceedings of the Symposium of the International Society of Rock Mechanics, Nancy, France. 1: 132-150. Cundall P A, Strack O D L. 1979. A Discrete Numerical Model for Granular Assemblies. Geotechnique, 29:47-65 doi: 10.1680/geot.1979.29.1.47 Cundall P A. 1982. Adaptive Density-Scaling for Time-Explicit Calculations//Proceedings of the 4th Inter-national Conference on Numerical Methods in Geomechanics (Edmonton, 1982) , 1, Rotterdam: Balkema:23-26. Deen N G W, Dijkhuizen W, Bokkers G A. 2004. Validation of the granular temperature prediction of the kinetic theory of granular flow by particle image velocimetry and discrete particle model//The Third International Symposium on Two-Phase flow Modelling and experimentation: 22-23. Di Renzo A, Di Maio F P. 2004. Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chemical Engineering Science, 59: 525-541 doi: 10.1016/j.ces.2003.09.037 Domenico S N. 1977. Elastic properties of unconsolidated porous sand reservoirs. Geophysics, 42: 1339-1368 doi: 10.1190/1.1440797 Dong Y, Zhang G, Sun Q, Zhao X, Niu X. 2015. Analysis of low-frequency vibrational modes and particle rearrangements in marginally jammed amorphous solid under quasi-static shear. Chinese Physical Letters, 32: 126201 doi: 10.1088/0256-307X/32/12/126201 Dzubiella J, Hoffmann G P, Löwen H. 2002. Lane formation in colloidal mixtures driven by an external field. Physical Review E, 65, 021402 https://www.researchgate.net/publication/11497618_Lan e formation in colloidal mixtures driven by an external fieldGan J, Zhou Z, Yu A B. 2016. Particle scale study of heat transfer in packed and fluidized beds of ellipsoidal particles. Chemical Engineering Science, 144: 201-215 doi: 10.1016/j.ces.2016.01.041 Goodrich C P, Liu A J, Nagel S R. 2014. Solids between the mechanical extremes of order and disorder. Nature Physics, 10: 578-581 doi: 10.1038/nphys3006 Helbing D. 2001. Traffic and related self-driven many-particle systems. Review of Modern Physics, 73:1067-1141 doi: 10.1103/RevModPhys.73.1067 Hoomans B P B. 1999. Granular dynamics of gas-solid two-phase flows. [PhD Thesis]. Nertherland:University of Twente. Hussainova I, Kubarsepp J, Shcheglov I. 1999. Investigation of impact of solid particles against hardmetal and cement targets. Tribology International, 32: 337-344 doi: 10.1016/S0301-679X(99)00073-0 Iwashita K, Oda M. 1998. Rolling resistance at contacts in simulation of shear band development by DEM. Journal of Engineering Mechanics, 124: 285-292 doi: 10.1061/(ASCE)0733-9399(1998)124:3(285) Iwashita K, Oda M. 2000. Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technology, 109: 192-205 doi: 10.1016/S0032-5910(99)00236-3 Jaeger H M, Nagel S R, Behringer R P. 1996. Granular solids, liquids, and gases. Review of Modern Physics, 68: 1259-1273 doi: 10.1103/RevModPhys.68.1259 Jefferson G, Haritos G K, McMeeking R M. 2002. The elastic response of a cohesive aggregate-a discrete element model with coupled particle interaction. Journal of the Mechanics and Physics of Solids, 50:2539-2575 doi: 10.1016/S0022-5096(02)00051-0 Jiang M J, Yu H S, Harris D. 2005. A novel discrete model for granular material incorporating rolling resistance. Computers and Geotechnics, 32: 340-357 doi: 10.1016/j.compgeo.2005.05.001 Jia X, Caroli C, Velicky B. 1999. Ultrasound propagation in externally stressed granular media. Physical Review Letters, 82: 1863-1866 doi: 10.1103/PhysRevLett.82.1863 Jiang Y M, Liu M. 2009. Granular solid hydrodynamics. Granular Matter, 11: 139-156 doi: 10.1007/s10035-009-0137-3 Johnson K L. 1985. Contact Mechanics. England: Cambridge University Press Khidas Y, Jia X 2010. Anisotropic nonlinear elasticity in a spherical-bead pack: Influence of the fabric anisotropy. Physical Review E, 81: 021303 doi: 10.1103/PhysRevE.81.021303 Kolymbas D, Wu W. 2000. Introduction to hypoplasticity. Modern Approaches to Plasticity, 1: 213-223 Kuhn M R. 1999. Structured deformation in granular materials. Mechanics of Materials, 31: 407-429 doi: 10.1016/S0167-6636(99)00010-1 Kruggel-Emden H, Smisek E, Rickelt S, Wirtz S, Scherer V. 2007. Review and extension of normal force models for the discrete element method. Powder Technology, 171: 157-173 doi: 10.1016/j.powtec.2006.10.004 Kruggel-Emden H, Wirtz S, Scherer V. 2008. A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior. Chemical Engineering Science, 63: 1523-1541 doi: 10.1016/j.ces.2007.11.025 Kuwabara G, Kono K. 1987. Restitution coefficient in collision between two spheres. Japanese Journal of Applied Physics, 26: 1230-1233 doi: 10.1143/JJAP.26.1230 Langston, P A, Tuzun U, Heyes D M. 1994. Continuous potential discrete particle simulations of stress and velocity-fields in hoppers|transition from fluid to granular flow. Chemical Engineering Science, 49, 1259-1275 doi: 10.1016/0009-2509(94)85095-X Lee J, Herrmann H J. 1993. Angle of repose and angle of marginal stability|molecular-dynamics of granular particles. Journal of Physics A, 26: 373-383 doi: 10.1088/0305-4470/26/2/021 Lherminier S, Planet R, Simon G, Vanel L, Ramos O. 2014. Revealing the structure of a granular medium through ballistic sound propagation. Physical Review Letters, 113: 098001 doi: 10.1103/PhysRevLett.113.098001 Li R, Yang H, Zheng G, Zhang B F, Fei M L, Sun Q C. 2016. Double speckle-visibility spectroscopy for the dynamics of a passive layer in a rotating drum.Powder Technology, 295: 167-174 doi: 10.1016/j.powtec.2016.03.031 Li X, Li X S. 2009. Micro-macro quantification of the internal structure of granular materials. Journal of Engineering Mechanics, 135: 641-656 doi: 10.1061/(ASCE)0733-9399(2009)135:7(641) Liu A J, Nagel S R. 1998. Jamming is not just cool any more. Nature, 396: 21-22 doi: 10.1038/23819 Liu A J, Nagel S R. 2010. The jamming transition and the marginally jammed solid. Annual Review of Condensed Matter Physics, 1: 347-369 doi: 10.1146/annurev-conmatphys-070909-104045 Liu J, Sun Q, Jin F. 2009. Visualization of force networks in 2D dense granular materials. Frontiers of Architecture and Civil Engineering in China, 4: 109-115 Liu X, Ge W, Li J. 2008. Non-equilibrium phase transitions in suspensions of oppositely driven inertial particles. Powder Technology, 184: 224-231 doi: 10.1016/j.powtec.2007.11.045 Liu X, Martin C L, Delette G, Bouvard D. 2010. Elasticity and strength of partially sintered ceramics. Journal of the Mechanics and Physics of Solids, 58: 829-842 doi: 10.1016/j.jmps.2010.04.007 Liu X, Martin C L, Bouvard D, Di Iorio S, Laurencin J, Delette G. 2011a. Strength of highly porous ceramic electraodes. Journal of the American Ceramic Society, 94: 3500-3508 doi: 10.1111/j.1551-2916.2011.04669.x Liu X, Martin C L, Delette G, Laurencin J, Bouvard D, Delahaye T. 2011b. Microstructure of porous composite electrodes generated by the discrete element method. Journal of Power Sources, 196: 2046-2054 doi: 10.1016/j.jpowsour.2010.09.033 Liu X, Papon A, Muhlhaus H. 2012. A numerical study of structural evolution in shear band. Philosophical Magazine, 92: 3501-3519 doi: 10.1080/14786435.2012.715249 Lu G, Third J R, Muller C. R. 2015. Discrete element models for non-spherical particle systems: From theoretical developments to applications. Chemical Engineering Science, 127: 425-465 doi: 10.1016/j.ces.2014.11.050 Luding S, Clément E, Blumen A, Rajchenbach J, Duran J. 1994. Anomalous energy dissipation in molecular dynamics simulations of grains: The "detachment" effect. Physical Review E, 50, 4113-4122 doi: 10.1103/PhysRevE.50.4113 Luding S. 1998. Collisions and contacts between two particles//Herrmann H J, Hovi J P, Luding S. (Eds.). Physics of Dry Granular Media, Kluwer Academic Publs, Dordrecht.: 285-304. Luding S. 2008a. Introduction to discrete element methods. European Journal of Environmental and Civil Engineering, 12: 785-826 doi: 10.1080/19648189.2008.9693050 Luding S. 2008b. Cohesive, frictional powders: contact models for tension. Granular matter, 10: 235-246 doi: 10.1007/s10035-008-0099-x Makse H A, Gland N, Johnson D L, Schwartz L. 2004. Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics. Physical Review E, 70: 061302 doi: 10.1103/PhysRevE.70.061302 Manning M, Liu A. 2011. Vibrational modes identify soft spots in a sheared disordered packing. Physical Review Letters, 107: 108302 doi: 10.1103/PhysRevLett.107.108302 Martin C L. 2004. Elasticity, fracture and yielding of cold compacted metal powders. Journal of the Mechanics and Physics of solids, 52: 1691-1717 doi: 10.1016/j.jmps.2004.03.004 Maw N, Barber J R, Fawcett J N. 1976. The oblique impact of elastic spheres. Wear, 38: 101-114 doi: 10.1016/0043-1648(76)90201-5 McNamara S, Garcia-Rojo R, Herrmann H J. 2008. Microscopic origin of granular ratcheting. Physical Review E, 77: 031304 doi: 10.1103/PhysRevE.77.031304 Merkel A, Tournat V, Gusev V 2014. Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity. Physical Review E, 90: 023206 doi: 10.1103/PhysRevE.90.023206 Meyer H, Schulmann N, Zabel J E, Wittmer J P. 2011. The structure factor of dense two-dimensional polymer solutions. Computer Physics Communications, 182: 1949-1953 doi: 10.1016/j.cpc.2010.12.003 Mindlin R D, Deresiewicz H. 1953. Elastic spheres in contact under varying oblique forces. Journal of Applied Mechanics, 20: 327-344 http://www.worldcat.org/title/elastic-spheres-in-contact-under-varying-oblique-forces/oclc/504883595 Mishra B K. 2003a. A review of computer simulation of bumbling mills by the discrete element method:part I|contact mechanics. International Journal of Mineral Processing, 71: 73-93 doi: 10.1016/S0301-7516(03)00032-2 Mishra B K. 2003b. A review of computer simulation of bumbling mills by the discrete element method:part II|practical applications. International Journal of Mineral Processing, 71: 95-112 doi: 10.1016/S0301-7516(03)00031-0 Misra A, Cheung J. 1999. Particle motion and energy distribution in tumbling ball mills. Powder Technology, 105: 222-227 doi: 10.1016/S0032-5910(99)00141-2 O'Hern C S, Silbert L E, Liu A J, Nagel S R. 2003. Jamming at zero temperature and zero applied stress:the epitome of disorder. Physical Review E, 68: 011306 doi: 10.1103/PhysRevE.68.011306 Peng Y, Wang Z, Alsayed A M, Yodh A G, Han Y. 2010. Melting of colloidal crystal films. Physical Review Letters, 104: 205703 doi: 10.1103/PhysRevLett.104.205703 Renaud G, Calle S, Defontaine M 2010. Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads. The Journal of the Acoustical Society of America, 128: 3344-3354 doi: 10.1121/1.3502461 Rognon P G, Roux J N, Naaim M, Chevoir F. 2008. Dense flows of cohesive granular materials. Journal of Fluid Mechanics, 596: 21-47 Sadd M H, Tai Q M. 1993. A contact law effects on wave-propagation in particulate materials using distinct element modeling. International journal of Non-Linear Mechanics, 28: 251-265 doi: 10.1016/0020-7462(93)90061-O Schafer J, Dippel S, Wolf D E. 1996. Force schemes in simulations of granular materials. Journal de Physique, 16: 5-20 https://www.researchgate.net/publication/41713396_Force_Scheme s in_Simulations of_Granular_MaterialsSchoenholz S S, Liu A J, Riggleman R A, Rottler J. 2014. Understanding plastic deformation in thermal glasses from single-soft-spot dynamics. Physical Review X, 4: 031014 https://www.researchgate.net/profile/Samuel_Schoenholz/publication/261439589_Understanding_Plastic_Deformatio n in_Thermal_Glasses from_Single-Soft-Spot_Dynamics/links/54b3d6b30cf2318f0f968d8a.pdf?inViewer=true&pdfJsDownload=true&disableCoverPage=true&origin=publication detailSilbert L E, Silbert M. 2009. Long-wavelength structural anomalies in jammed systems. Physical Review E, 80: 041304 doi: 10.1103/PhysRevE.80.041304 Song C, Wang P, Makse H A. 2008. A phase diagram for jammed matter. Nature, 453: 629-632 doi: 10.1038/nature06981 Sun Q, Jin F, Wang G, Song S, Zhang G. 2015. On granular elasticity. Scientific Reports, 5: 9652 doi: 10.1038/srep09652 Tanguy A, Mantisi B, Tsamados M. 2010. Vibrational modes as a predictor for plasticity in a model glass. European Physical Letters, 90: 16004 doi: 10.1209/0295-5075/90/16004 Tejada I G, Jimenez R. 2014. Impact of the timestep in some molecular dynamics simulations on compression of granular systems. European Physical Journal E, 37: 15 doi: 10.1140/epje/i2014-14015-4 Thornton C, Yin K K. 1991. Impact of elastic spheres with and without adhesion. Powder Technology, 65:153-166 doi: 10.1016/0032-5910(91)80178-L Thornton C. 1997. Coefficient of restitution for collinear collisions of elastic perfectly plastic spheres. Journal of Applied Mechanics, 64: 383-386 doi: 10.1115/1.2787319 Thornton C, Cummins S J, Cleary P W. 2011. An investigation of the comparative behaviour of alternative contact force models during elastic collisions. Powder Technology, 210: 189-197 doi: 10.1016/j.powtec.2011.01.013 Thornton C, Cummins S J, Cleary P W. 2013. An investigation of the comparative behaviour of alternative contact force models during inelastic collisions. Powder technology, 233: 30-46 doi: 10.1016/j.powtec.2012.08.012 Tighe B. 2011. Relaxations and rheology near Jamming.Physical Review Letters, 107: 158303 doi: 10.1103/PhysRevLett.107.158303 Tordesillas A, Muthuswamy M, Walsh S D. 2008. Mesoscale measures of nona±ne deformation in dense granular assemblies. Journal of Engineering Mechanics, 134: 1095-1113 doi: 10.1061/(ASCE)0733-9399(2008)134:12(1095) Tsuji Y, Tanaka T, Ishida T. 1992. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology, 71: 239-250 doi: 10.1016/0032-5910(92)88030-L Utter B, Behringer R P. 2004. Self-diffusion in dense granular shear flows. Physical Review E, 69: 031308 doi: 10.1103/PhysRevE.69.031308 Vitelli V. 2010. Attenuation of shear sound waves in jammed solids. Soft Matter, 6: 3007-3012 doi: 10.1039/c000834f Vu-Quoc L, Zhang X, Lesburg L. 2001. Normal and tangential force-displacement relations for frictional elasto-plastic contact of spheres. International Journal of Solids and Structures, 38: 6455-6489 doi: 10.1016/S0020-7683(01)00065-8 Vu-Quoc L, Zhang X. 1999. An accurate and e±cient tangential force-displacement model for elastic fric-tional contact in particle-flow simulations. Mechanics of Materials, 31: 235-269 doi: 10.1016/S0167-6636(98)00064-7 Wang X, Zheng W, Wang L, Xu N. 2015. Disordered solids without well-defined transverse phonons: the nature of hard-sphere glasses. Physical Review Letters, 114: 035502 doi: 10.1103/PhysRevLett.114.035502 Wang P J, Li Y D, Xia J H, Liu C S. 2008a. Characterization of reflection intermittency in a composite granular chain. Physical Review E, 77: 060301 Wang P, Song C, Briscoe C. 2008b. Particle dynamics and effective temperature of jammed granular matter in a slowly sheared three-dimensional Couette cell. Physical Review E, 77: 061309 doi: 10.1103/PhysRevE.77.061309 Wang P J, Xia J H, Li Y D, Liu C S. 2007. Crossover in the power-law behavior of confined energy in a composite granular chain. Physical Review E, 76: 041305 doi: 10.1103/PhysRevE.76.041305 Walton O R, Braun R L. 1986. Viscosity, granular temperature and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology, 30: 949-980 doi: 10.1122/1.549893 Walton O R. 1993. Numerical simulation of cline chute flows of monodisperse, inelastic, frictional spheres. Mechanics of Materials, 16: 239-247 doi: 10.1016/0167-6636(93)90048-V Wang Y, Steffen A, Latham S, Mora P. 2006. Implementation of particle-scale rotation in the 3-D lattice model. Pure and Applied Geophysics, 163: 1769-1785 doi: 10.1007/s00024-006-0096-0 Warr S, Hansen J P. 1996. Relaxation of local density fluctuations in a fluidized granular medium. Euro-physics Letters, 36: 589-594 doi: 10.1209/epl/i1996-00273-1 Wen P P, Zheng N, Li L S, Li H, Sun G, Shi Q F. 2012. Polymerlike statistical characterization of two-dimensional granular chains. Physical Review E, 85: 031301 doi: 10.1103/PhysRevE.85.031301 Wildman R D, Huntley J M, Parker D J. 2001. Granular temperature profiles in three-dimensional vibroflu-idized granular beds. Physical Review E, 63: 061311 doi: 10.1103/PhysRevE.63.061311 Xia C, Li J, Cao Y, Kou B, Xiao X, Fezzaa K, Xiao T,Wang Y. 2015. The structural origin of the hard-sphere glass transition in granular packing. Nature Communications, 6: 1-9 https://www.researchgate.net/profile/Yujie_Wang5/publication/282247305_Th e structural origin of the hard-sphere glass transition in granular packing/links/560923d408ae576ce63dda8e.pdf?inViewer=true&pdfJsDownload=true&disableCoverPage=true&origin=publication detailXu B H, Yu A B. 1997. Numerical simulation of the gas-solid flow in a fluidised bed by combining discrete particle method with computational fluid dynamics. Chemical Engineering Science, 52: 2785-2809 doi: 10.1016/S0009-2509(97)00081-X Xu N. 2011. Mechanical, vibrational, and dynamical properties of amorphous systems near jamming. Fron-tiers of Physics, 6: 109-123 doi: 10.1007/s11467-010-0102-y Xu N, Vitelli V, Liu A J, Nagel S R. 2010. Anharmonic and quasi-localized vibrations in jammed solids-modes for mechanical failure. Europhysics Letters, 90: 56001 doi: 10.1209/0295-5075/90/56001 Xu N, Ching E S C. 2010. Effects of particle-size ratio on jamming of binary mixtures at zero temperature.Soft Matter, 6: 2944-2948 doi: 10.1039/b926696h Yang H, Li R, Kong P, Sun QC, Biggs MJ, Zivkovic V. 2015. Avalanche dynamics of granular materials under the slumping regime in a rotating drum as revealed by speckle visibility spectroscopy. Physical Review E, 91: 042206 doi: 10.1103/PhysRevE.91.042206 Ye M. 2005. Multi-level modeling of dense gas-solid two-phase flows. [PhD Thesis]. Nertherland: University of Twente. Zaccone A, Terentjev E M. 2014.Short-range correlations control the G/K and Poisson ratios of amorphous solids and metallic glasses. Journal of Applied Physics, 115: 033510 doi: 10.1063/1.4862403 Zhang Q, Li Y, Hou M, Jiang Y, Liu M. 2012. Elastic waves in the presence of a granular shear band formed by direct shear. Physical Review E, 85: 031306 doi: 10.1103/PhysRevE.85.031306 Zhang Z X, Xu N, Chen D T N, Yunker P, Alsayed A M, Aptowicz K B, Habdas P, Liu A J, Nagel S R,Yodh A G. 2009. Thermal vestige of the zero-temperature jamming transition. Nature, 459: 230-233 doi: 10.1038/nature07998 Zheng H P. 2014. Properties of surface waves in granular media under gravity. Chinese Physics B, 23:054503 doi: 10.1088/1674-1056/23/5/054503 Zhou Y H. 2013. Modeling of softsphere normal collisions with characteristic of coe±cient of restitution dependent on impact velocity. Theoretical and Applied Mechanics Letters, 3: 021003 doi: 10.1063/2.1302103 Zhou Y C, Wright B D, Yang R Y, Xu B H, Yu A B. 1999. Rolling friction in the dynamic simulation of sandpile formation. Physica A, 269: 536-553 doi: 10.1016/S0378-4371(99)00183-1 Zhu H P, Yu A B. 2003. The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow. Physica A, 325: 347-360 doi: 10.1016/S0378-4371(03)00143-2 Zhu H P, Zhou Z Y, Yang R Y, Yu A B. 2007. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science, 62: 3378-3396 doi: 10.1016/j.ces.2006.12.089 Zhu H P, Zhou Z Y, Yang R Y, Yu A B. 2008. Discrete particle simulation of particulate systems: A review of major applications and findings. Chemical Engineering Science, 63: 5728-5770 doi: 10.1016/j.ces.2008.08.006 -
下载:
图(16) / 表(2)
计量
- 文章访问数: 3371
- HTML全文浏览量: 696
- PDF下载量: 1960
- 被引次数: 0
