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颗粒介质弹性的弛豫

孙其诚 刘传奇 周公旦

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颗粒介质弹性的弛豫

孙其诚, 刘传奇, 周公旦

Relaxation of granular elasticity

Sun Qi-Cheng, Liu Chuan-Qi, Gordon G D Zhou
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  • 颗粒介质是复杂的多体相互作用体系, 其弹性源自内部的力链结构, 弹性能量处在亚稳态, 具有复杂的弛豫行为. 在常规作用下, 颗粒介质往往呈现明显的弹性弛豫. 应力松弛是应变恒定时应力的衰减现象, 弹性弛豫是应力松弛的主要原因. 在前期工作基础上, 从弹性势能面和双颗粒温度热力学角度分析了弹性弛豫的机理, 量化了弹性应力演化不可逆过程; 基于双颗粒温度热力学计算得到了弹性能、颗粒温度和应力的演化, 其中应力松弛的计算结果与实验结果基本一致, 讨论了颗粒温度初值和输运系数的影响. 指出, 开展力链结构及其动力学研究是揭示宏观弹性弛豫机理的关键.
    In granular materials, particles constitute a complex force chains network through contact with each other, and elastic energies are stored due to deformation of particles. This elastic behavior is macroscopic manifestation of inter-particle contacts. Elastic constants or elastic moduli are of fundamental importance for granular material. Due to the hyper-static property of inter-particle forces, the bulk elastic energy stored in the contacts is metastable in the viewpoint of energy landscape, i.e. a high energy state may approaches a more stable state (i.e. relatively lower state) under the action of external perturbations or internal stress, resulting in the elastic modulus reduction. This process is the so-called elasticity relaxation. It may be more obvious in granular materials.The time-dependent behavior of granular materials, especially the creep, has been studied in experiments and numerical simulations, while the stress relaxation has few reported investigations. Stress relaxation is defined as the process in vohich the initial strain is maintained and the stress decays with the time. From energetic viewpoint, elastic energy is stored in the deformation of particles. The granular system is in a metastable state when confined in a state easy to break the balance. Generally speaking, the shape and grading of particles, volume fraction, surface friction properties, initial structure features, ageing time, loading strain rate will all play important roles in stress relaxation.In this work, it is believed that the elastic relaxation is the only mechanism to describe the stress relaxation, and the mechanism of it is analyzed from the viewpoint of the potential energy surface. Stress relaxation is calculated by means of the so-called two-granular temperature theory (TGT) we developed previously (Sun Q et al. 2015 Sci. Rep. 5 9652). The stress decays fast at the beginning, then decreases gradually slowly to a stable value. The logarithmic fit is first proposed to describe the stress decay in the compressed system. Calculated results of stress relaxation match well with the measured results in a recently published paper (Miksic A, Alava M J 2013 Phys. Rev. E 88 032207). Both elastic energy and granular temperature may be reduced with increasing time. It is found that the initial value of the granular temperature has a great influence on the stress relaxation, and at present its effect is input by trial and error. It would be a major problem how to determine the initial value of the granular temperature. Moreover, the relaxation coefficient of elastic stress is basically chosen as a function of granular temperature which is described by the Arrhenius equation that need be further investigated.
      通信作者: 孙其诚, qcsun@tsinghua.edu.cn
    • 基金项目: 国家自然科学基金项目(批准号: 11272048, 51239006)、欧盟 Marie Curie 国际项目(批准号: IRSES-294976)、美国全球创新计划(Global Innovation Initiative)和清华大学自主科研计划资助的课题.
      Corresponding author: Sun Qi-Cheng, qcsun@tsinghua.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272048, 51239006), the European Commission Marie Curie Actions (Grant No. IRSES-294976), the Global Innovation Initiative of US, and Tsinghua University Initiative Scientific Research Program.
    [1]

    Sun Q 2015 Acta Phys. Sin. 64 076101 (in Chinese) [孙其诚 2015 物理学报 64 076101]

    [2]

    Jiang Y M, Liu M 2009 Granular Matter 11 139

    [3]

    Savage S B, Jeffrey D J 1981 J. Fluid Mech. 110 255

    [4]

    Lun C K K, Savage S B, Jeffrey D J, Chepurniy N 1984 J. Fluid Mech. 140 223

    [5]

    Goldhirsch I 2003 Annual Rev Fluid Mech. 35 267

    [6]

    Forterre Y, Pouliquen O 2008 Annual Rev Fluid Mech. 40 1

    [7]

    Chialvo S, Sun J, Sundaresan S 2012 Phys. Rev. E 85 021305

    [8]

    Tighe B P, Vlugt T J H 2011 J. Stat. Mech.P04002

    [9]

    Sun Q, Jin F, Wang G, Song S, Zhang G 2015 Sci. Rep. 5 9652

    [10]

    Wales D J 2003 Energy landscapes (Cambridge: Cambridge University Press) p1

    [11]

    Stillinger F H 1995 Science 267 1935

    [12]

    Miksic A, Alava M J 2013 Phys. Rev. E 88 032207

    [13]

    Jiang Y M, Liu M 2015 Europhys. J. E 38 15

    [14]

    Xu N 2011 Front. Phys. China 6 109

    [15]

    Collins I F, Houlsby G T 1997 Proceed. Royal Soc. A 453 1975

    [16]

    Jenkins J T 2006 Phys. Fluids 18 103307

  • [1]

    Sun Q 2015 Acta Phys. Sin. 64 076101 (in Chinese) [孙其诚 2015 物理学报 64 076101]

    [2]

    Jiang Y M, Liu M 2009 Granular Matter 11 139

    [3]

    Savage S B, Jeffrey D J 1981 J. Fluid Mech. 110 255

    [4]

    Lun C K K, Savage S B, Jeffrey D J, Chepurniy N 1984 J. Fluid Mech. 140 223

    [5]

    Goldhirsch I 2003 Annual Rev Fluid Mech. 35 267

    [6]

    Forterre Y, Pouliquen O 2008 Annual Rev Fluid Mech. 40 1

    [7]

    Chialvo S, Sun J, Sundaresan S 2012 Phys. Rev. E 85 021305

    [8]

    Tighe B P, Vlugt T J H 2011 J. Stat. Mech.P04002

    [9]

    Sun Q, Jin F, Wang G, Song S, Zhang G 2015 Sci. Rep. 5 9652

    [10]

    Wales D J 2003 Energy landscapes (Cambridge: Cambridge University Press) p1

    [11]

    Stillinger F H 1995 Science 267 1935

    [12]

    Miksic A, Alava M J 2013 Phys. Rev. E 88 032207

    [13]

    Jiang Y M, Liu M 2015 Europhys. J. E 38 15

    [14]

    Xu N 2011 Front. Phys. China 6 109

    [15]

    Collins I F, Houlsby G T 1997 Proceed. Royal Soc. A 453 1975

    [16]

    Jenkins J T 2006 Phys. Fluids 18 103307

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出版历程
  • 收稿日期:  2015-04-13
  • 修回日期:  2015-07-22
  • 刊出日期:  2015-12-05

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