颗粒材料破碎演化路径细观热力学机制

沈超敏; 刘斯宏

doi:10.6052/0459-1879-18-340

颗粒材料破碎演化路径细观热力学机制

doi: 10.6052/0459-1879-18-340

沈超敏,
刘斯宏^2),

河海大学水利水电学院,南京 210098

基金项目: 1) 国家自然科学基金(U1765205),国家重点研发计划(2017YFC0404800)以及中央高校基本科研业务费专项资金(2018B40914)资助项目.

详细信息

作者简介:
作者简介: 2) 刘斯宏,教授,博导,主要研究方向：土石坝工程、粒状体力学与土工袋技术. E-mail: Sihongliu@hhu.edu.cn

中图分类号: TV16;
计量
- 文章访问数: 2079
- HTML全文浏览量: 111
- PDF下载量: 331
- 被引次数: 0
出版历程
- 刊出日期: 2019-01-18

EVOLUTION PATH FOR THE PARTICLE BREAKAGE OF GRANULAR MATERIALS: A MICROMECHANICAL AND THERMODYNAMIC INSIGHT

Shen Chaomin,
Liu Sihong^{2)
,}

Department of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China

摘要

摘要: 颗粒材料在高应力环境下会发生颗粒破碎现象,颗粒破碎不仅影响颗粒材料的力学特性,同时与大量工程问题密切相关.目前的相关研究主要集中在唯象地描述颗粒破碎的演化以及破碎对力学特性的影响层面,对颗粒破碎演化路径的物理机制研究较少.本文基于热力学框架,采用细观力学中细观-宏观的均匀化方法推导了颗粒体系弹性能和破碎能量耗散,并在最大能量耗散的假设下,在热力学框架内,建立了理想化的无摩擦球体颗粒等向压缩过程的弹性-破碎模型,阐述了颗粒材料破碎演化路径细观热力学机制.由于模型的推导不依赖任何唯象的经验公式,因此模型中包含的参数均有明确的物理意义.模型预测与前人试验结果对比表明,材料的初始级配对弹性压缩模量和破碎应力的影响并不相同：不同分形维数级配对应的弹性体变模量存在极大值,而破碎应力却随着分形维数的增大单调递增;颗粒破碎的演化符合最大能量耗散原理,且颗粒材料的压缩曲线可以分为弹性-破碎-拟弹性3个机制不同的阶段.
- 颗粒材料 /
- 颗粒破碎 /
- 级配 /
- 热力学 /
- 细观力学
Abstract: Particle breakage of granular materials is ubiquitous in nature and engineering practices and often takes place under high stress levels. The phenomenon of particle breakage may not only influence the mechanical response of granular materials, resulting the contraction of the volume of the material and reduction of the shearing strength, but is also closely associated to a variety of engineering problems. The existing research is mainly focused on depicting the evolution of the particle breakage and uses a quantifiable parameter to relate the particle breakage to the subsequent mechanical response. However, little attention has been paid to exploring the underlying physics of the driving force that initiates and attenuates the particle breakage. In this study, we present the formulation of an elastic-breakage model for the isotropic compression of frictionless spheres in the framework of thermodynamics. In the model, both the elastic strain energy and the dissipation due to particle breakage are formulated using the micro-macro averaging procedure, which is often used in micromechanics of granular materials. The evolution path of the particle breakage is determined using the maximum energy dissipation hypothesis. As the modelling does not involve any empirical results, all the model parameters have concrete physical meanings. Comparison of the model prediction with the experimental data in the literature showed that the initial gradation has different effects on the elastic bulk modulus and the breakage stress: the bulk modulus increase initially and then decrease with the fractal dimension of the gradation, which implies that there is a peak bulk modulus for a certain value of the fractal dimension; while the breakage stress increases monotonically with the increase of the fractal dimension. In addition, both the bulk modulus and the breakage stress increase monotonically with the increase of the polydispersity of the particle sizes. The evolution path of the gradation due to particle breakage is found to indeed satisfy the maximum dissipation hypothesis. Both experimental results and model prediction show that the compression curve of granular materials can be divided into three stages: the elastic compression stage under low compressive stress, particle breakage stage and the pseudoelastic compression after sufficiently large amount of particle breakage.
- granular material /
- particle breakage /
- gradation /
- thermodynamics /
- micromechanics

HTML全文

参考文献(1)

[1]	王增会, 李锡夔. 基于介观力学信息的颗粒材料损伤--愈合与塑性宏观表征. 力学学报, 2018, 50(2): 284-296
[1]	(Wang Zenghui, Li Xikui.Meso-mechanically informed macroscopic characterization of damage-healing-plasticity for granular materials. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 284-296 (in Chinese))
[2]	Fu Z, Chen S, Wang T.Predicting the earthquake-induced permanent deformation of concrete face rockfill dams using the strain-potential concept in the finite-element method. International Journal of Geomechanics, 2017, 17(11): 04017100
[3]	Zhou JW, Liu Y, Du CL, et al.Effect of the particle shape and swirling intensity on the breakage of lump coal particle in pneumatic conveying. Powder Technology, 2017, 317: 438-48
[4]	姚仰平, 张民生, 万征等. 基于临界状态的砂土本构模型研究. 力学学报, 2018, 50(3): 589-598
[4]	(Yao Yangping, Zhang Minsheng, Wan Zheng, et al.Constitutive model for sand based on the critical state. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 589-598 (in Chinese))
[5]	万征, 孟达. 复杂加载条件下的砂土本构模型. 力学学报, 2018, 50(4): 929-948
[5]	(Wan Zheng, Meng Da.A constitutive model for sand under complex loading conditions. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 929-948(in Chinese))
[6]	Nakata A, Hyde M, Hyodo H, et al.A probabilistic approach to sand particle crushing in the triaxial test. Géotechnique, 1999, 49(5): 567-583
[7]	Zheng W, Tannant DD.Grain breakage criteria for discrete element models of sand crushing under one-dimensional compression. Computers and Geotechnics, 2018, 95: 231-239
[8]	Hagerty M, Hite D, Ullrich C, et al.One-dimensional high-pressure compression of granular media. Journal of Geotechnical Engineering, 1993, 119(1): 1-18
[9]	Cheng Y, Bolton M, Nakata Y.Grain crushing and critical states observed in DEM simulations. Powders & Grains, 2005, 2: 1393-1397
[10]	Robertson D.Computer simulations of crushable aggregates. [PhD Thesis]. Cambridge: University of Cambridge, 2000
[11]	Liu Y, Liu H, Mao H.DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials. Computers and Geotechnics, 2017, 84: 58-67
[12]	Wang J, Yan H.DEM analysis of energy dissipation in crushable soils. Soils and Foundations, 2012, 52(2): 644-657
[13]	Ciantia M, Arroyo Alvarez De Toledo M, Calvetti F, et al. An approach to enhance efficiency of DEM modelling of soils with crushable grains. Géotechnique, 2015, 65(2): 91-110
[14]	Ciantia MO, Arroyo M, Calvetti F, et al.A numerical investigation of the incremental behavior of crushable granular soils. International Journal for Numerical and Analytical Methods in Geomechanics, 2016, 40(13): 1773-1798
[15]	Einav I.Fracture propagation in brittle granular matter. Proceedings of the Royal Society A: Mathematical,Physical and Engineering Sciences, 2007, 463(2087): 3021-3035
[16]	Ben-Nun O, Einav I, Tordesillas A.Force attractor in confined comminution of granular materials. Physical Review Letters, 2010, 104(10): 108001
[17]	Ma G, Zhou W, Regueiro RA, et al.Modeling the fragmentation of rock grains using computed tomography and combined FDEM. Powder Technology, 2017, 308: 388-397
[18]	Zhou M, Song E.A random virtual crack DEM model for creep behavior of rockfill based on the subcritical crack propagation theory. Acta Geotechnica, 2016, 11(4): 827-847
[19]	Mcdowell G, Bolton M.On the micromechanics of crushable aggregates. Géotechnique, 1998, 48(5): 667-679
[20]	Mcdowell G, Bolton M, Robertson D.The fractal crushing of granular materials. Journal of the Mechanics and Physics of Solids, 1996, 44(12): 2079-2101
[21]	Einav I.Breakage mechanics-Part I: Theory. Journal of the Mechanics and Physics of Solids, 2007, 55(6): 1274-1297
[22]	Einav I.Breakage mechanics-Part II: Modelling granular materials. Journal of the Mechanics and Physics of Solids, 2007, 55(6): 1298-1320
[23]	Zhang Y, Buscarnera G.Breakage mechanics for granular materials in surface-reactive environments. Journal of the Mechanics and Physics of Solids, 2018, 112: 89-108
[24]	Hardin BO.Crushing of soil particles. Journal of geotechnical engineering, 1985, 111(10): 1177-1192
[25]	Zhang X, Hu W, Scaringi G, et al.Particle shape factors and fractal dimension after large shear strains in carbonate sand. Géotechnique Letters, 2018, 8(1): 73-79
[26]	Tyler SW, Wheatcraft SW.Fractal scaling of soil particle-size distributions: analysis and limitations. Soil Science Society of America Journal, 1992, 56(2): 362-369
[27]	Johnson K, Kendall K, Roberts A.Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1971, 324(1558): 301-313
[28]	Shaebani MR, Madadi M, Luding S, et al.Influence of polydispersity on micromechanics of granular materials. Physical Review E, 2012, 85(1): 011301
[29]	Sufian A, Russell A, Whittle A.Anisotropy of contact networks in granular media and its influence on mobilised internal friction. Géotechnique, 2017, 67(12): 1067-1080
[30]	Mueth DM, Jaeger HM, Nagel SR.Force distribution in a granular medium. Physical Review E, 1998, 57(3): 3164
[31]	Ziegler H.An Introduction to Thermomechanics. Elsevier, 2012
[32]	Mesri G, Vardhanabhuti B.Compression of granular materials. Canadian Geotechnical Journal, 2009, 46(4): 369-392
[33]	尹振宇, 许强, 胡伟. 考虑颗粒破碎效应的粒状材料本构研究: 进展及发展. 岩土工程学报, 2012, 34(12): 2170-2180
[33]	(Yin Zhenyu, Xu Qiang, Hu Wei.Constitutive relations for granular materials considering particle crushing: Review and development. Chinese Journal of Geotechnical Engineering, 2012, 34(12): 2170-2180(in Chinese))
[34]	Collins IF, Houlsby GT.Application of thermomechanical principles to the modelling of geotechnical materials. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1997, 453(1964): 1975-2001
[35]	Pestana JM, Whittle A.Compression model for cohesionless soils. Géotechnique, 1995, 45(4): 611-632
[36]	Minh N, Cheng Y.A DEM investigation of the effect of particle-size distribution on one-dimensional compression. Géotechnique, 2013, 63(1): 44-53