搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

颗粒-颗粒接触力的热力学模型

蒋亦民 刘佑

引用本文:
Citation:

颗粒-颗粒接触力的热力学模型

蒋亦民, 刘佑

A thermodynamic model of grain-grain contact force

Jiang Yi-Min, Liu Mario
PDF
导出引用
  • 以颗粒二体接触力模型为基础和出发点的软球离散元模拟是当前颗粒物理和力学领域广泛应用的研究手段.但文献上经常使用的、包括著名的Hertz-Mindlin和Luding在内的力模型并没有完全明确弹性势能或耗散热的计算方法,故从热力学层面看它们还需要完善.考虑到机械能的耗散行为是这类材料的重要物理内容,本文借鉴近年来提出的颗粒固体流体动力学(GSH)思路,提出一种具有明确势能和热功率的接触力建模方法.该理论除明确给出了机械能和热能的计算公式外,还能具体描述能量守恒、热力学平衡态和熵增加等基本原理,解决了传统接触力模型在这些方面的欠缺问题.初步计算显示本文模型的恢复系数可以随碰撞速率的增加而减弱,这比现有的其他模型更符合实验观测.虽然为简单起见这些公式仅局限于二维和忽略颗粒转动运动情况,文中讨论了如何推广到三维含转动情形,以及所涉及的滚动和扭转接触力的热力学处理问题.鉴于是否在Onsager非平衡热力学基础上建模是本文给出的接触力公式有别于当前其他模型的关键所在,文中强调了这里的主要建模对象应该是热力学特征函数和Onsager迁移系数,而接触力是它们的推导结果.这是一个与目前直接针对接触力进行建模的不同思路.文中对颗粒物质特有的、反映样品几何变形与弹应变之间联络的一个非对角迁移系数做了详细介绍,并且认为它与打滑等复杂力学现象关系密切,无论宏观GSH尺度上,还是细观接触力尺度上都不可忽略.
    The starting premise of any soft discrete element method simulation, widely used in granular physics and granular mechanics, is the modelling of grain-grain contact force. Most of models often used in the literature including the famous ones by Hertz-Mindlin and Luding, do not present the algorigthy of total elastic potential, or the rate of dissipation which is mainly due to the partially frictional character of the forces. This renders the question of thermodynamic consistency unsettled. A model that possesses explicit expressions for both is proposed here. It is conceptually closely related to the continuum-mechanical theory of granular solid hydrodynarmics (GSH). This theory contains expressions for the total elastic potential and the thermal energy, it accounts for energy conservation and the positivity of entropy production, and it clarifies the equilibrium properties of granular media. All these are lacking (or hidden) in the contact models widely used in the literature. A preliminary calculation shows that the restitution coefficient varies with the impact velocity, which is an added bonus, and demonstrates the model's increased realism. For simplicity, the equations presented in this work are limited to the 2D-case and neglect granular rotations. Nevertheless, the generalization to the 3D-case and the inclusion of granular rotations are carefully discussed, clarifying how to treat rolling and the torsional forces in a thermodynamically consistent fashion. A key point of the present approach, and the major difference to other force models, is the fact that, starting from the characteristic thermodynamic potential, we employ the Onsager reciprocity relation to set up the transport coefficients. The contact forces (usually postulated) are then derived from them. This difference is both conceptually and methodologically relevant. We discussed in detail off-diagonal transport coefficients, especially the so called gear ratio that is particular to granular matter. It reflects the difference between the elastic and the total strain, and is closely related to the slip movement of contact surface, which occur during shear, rolling and torsional deformations. It is relevant to both the macroscopic GSH scales, and the mesoscopic granular scale.
    [1]

    Hertz H 1881 J. Reine Angew. Math. 92 156

    [2]

    Thornton C 2015 Granular Dynamics, Contact Mechanics and Particle System Simulations–A DEM Study (Particle Technology Series, Volume 24) (eBook DOI 10.1007/978-3-319-18711-2) (Switzerland:Springer International Publishing AG)

    [3]

    Laughlin R B, Pines D 2000 Proc. Natl. Acad. Sci. USA 97 28

    [4]

    Laughlin R B 2004 A Different Universe (Changsha:Hunan Science and Technology Press) (in Chinese)[王文浩 译 2008 不同的宇宙(长沙:湖南科学技术出版社)]

    [5]

    Luding S 2008 Granular Matter 10 235

    [6]

    Truesdell C 1972 Rational Thermodynamics (Berlin:Springer-Verlag)

    [7]

    Boussinesq J 1873 C. R. Hebd. Seances Acad. Sci. 77 1521

    [8]

    Bonneau L, Andreotti B, Clément E 2007 Phys. Rev. E 75 016602

    [9]

    Sun Q C, Jin F, Zhou G D 2013 Granular Matter 15 119

    [10]

    Kumar N 2014 Ph. D. Dissertation (Enschede:University of Twente. The Netherlands ISBN:978-90-365-3634-9, DOI:10.3990/1.9789036536349)

    [11]

    Jiang Y M, Liu M 2009 Granular Matter 11 139

    [12]

    Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Matter (Beijing:Science Press) (in Chinese)[孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京:科学出版社)]

    [13]

    Jiang Y M, Liu M 2014 Acta Mech. 225 2363

    [14]

    Jiang Y M, Liu M 2015 Eur. Phys. J. E 38 15

    [15]

    Jiang Y M, Liu M 2003 Phys. Rev. Lett. 91 144301

    [16]

    Jiang Y M, Liu M 2004 Phys. Rev. Lett. 93 148001

    [17]

    Jiang Y M, Liu M 2007 Phys. Rev. Lett. 99 105501

    [18]

    Torquato S, Stillinger F H 2010 Rev. Mod. Phys. 82 2633

    [19]

    Edwards S F, Mounfield C C 1996 Physica A 226 1

    [20]

    Edwards S F, Mounfield C C 1996 Physica A 226 12

    [21]

    Edwards S F, Mounfield C C 1996 Physica A 226 25

    [22]

    Parisi G, Zamponi F 2010 Rev. Mod. Phys. 82 789

    [23]

    Luding S 2009 Nonlinearity 22 R101

    [24]

    Hayakawa H, Otsuki M 2008 Prog. Theor. Phys. 119 381

    [25]

    Kuang S B, Zou R P, Pan R H, Yu A B 2012 Ind. Eng. Chem. Res. 51 14289

    [26]

    Hou Q F, Kuang S B, Yu A B 2017 Chem. Engineer. Sci. 161 67

  • [1]

    Hertz H 1881 J. Reine Angew. Math. 92 156

    [2]

    Thornton C 2015 Granular Dynamics, Contact Mechanics and Particle System Simulations–A DEM Study (Particle Technology Series, Volume 24) (eBook DOI 10.1007/978-3-319-18711-2) (Switzerland:Springer International Publishing AG)

    [3]

    Laughlin R B, Pines D 2000 Proc. Natl. Acad. Sci. USA 97 28

    [4]

    Laughlin R B 2004 A Different Universe (Changsha:Hunan Science and Technology Press) (in Chinese)[王文浩 译 2008 不同的宇宙(长沙:湖南科学技术出版社)]

    [5]

    Luding S 2008 Granular Matter 10 235

    [6]

    Truesdell C 1972 Rational Thermodynamics (Berlin:Springer-Verlag)

    [7]

    Boussinesq J 1873 C. R. Hebd. Seances Acad. Sci. 77 1521

    [8]

    Bonneau L, Andreotti B, Clément E 2007 Phys. Rev. E 75 016602

    [9]

    Sun Q C, Jin F, Zhou G D 2013 Granular Matter 15 119

    [10]

    Kumar N 2014 Ph. D. Dissertation (Enschede:University of Twente. The Netherlands ISBN:978-90-365-3634-9, DOI:10.3990/1.9789036536349)

    [11]

    Jiang Y M, Liu M 2009 Granular Matter 11 139

    [12]

    Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Matter (Beijing:Science Press) (in Chinese)[孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京:科学出版社)]

    [13]

    Jiang Y M, Liu M 2014 Acta Mech. 225 2363

    [14]

    Jiang Y M, Liu M 2015 Eur. Phys. J. E 38 15

    [15]

    Jiang Y M, Liu M 2003 Phys. Rev. Lett. 91 144301

    [16]

    Jiang Y M, Liu M 2004 Phys. Rev. Lett. 93 148001

    [17]

    Jiang Y M, Liu M 2007 Phys. Rev. Lett. 99 105501

    [18]

    Torquato S, Stillinger F H 2010 Rev. Mod. Phys. 82 2633

    [19]

    Edwards S F, Mounfield C C 1996 Physica A 226 1

    [20]

    Edwards S F, Mounfield C C 1996 Physica A 226 12

    [21]

    Edwards S F, Mounfield C C 1996 Physica A 226 25

    [22]

    Parisi G, Zamponi F 2010 Rev. Mod. Phys. 82 789

    [23]

    Luding S 2009 Nonlinearity 22 R101

    [24]

    Hayakawa H, Otsuki M 2008 Prog. Theor. Phys. 119 381

    [25]

    Kuang S B, Zou R P, Pan R H, Yu A B 2012 Ind. Eng. Chem. Res. 51 14289

    [26]

    Hou Q F, Kuang S B, Yu A B 2017 Chem. Engineer. Sci. 161 67

  • [1] 周益娴. 基于连续数值模拟的筒仓卸载过程中颗粒物压强及其速度场分析. 物理学报, 2019, 68(13): 134701. doi: 10.7498/aps.68.20182205
    [2] 程琦, 冉宪文, 刘苹, 汤文辉, Raphael Blumenfeld. 颗粒物质内自旋小球运动行为的数值模拟研究. 物理学报, 2018, 67(1): 014702. doi: 10.7498/aps.67.20171459
    [3] 许聪慧, 张国华, 钱志恒, 赵雪丹. 水平激励下颗粒物质的有效质量及耗散功率的研究. 物理学报, 2016, 65(23): 234501. doi: 10.7498/aps.65.234501
    [4] 吴迪平, 李星祥, 秦勤, 管奔, 臧勇. 离散颗粒层被横向推移过程中的力学行为研究. 物理学报, 2014, 63(9): 098201. doi: 10.7498/aps.63.098201
    [5] 彭政, 蒋亦民, 刘锐, 厚美瑛. 垂直振动激发下颗粒物质的能量耗散. 物理学报, 2013, 62(2): 024502. doi: 10.7498/aps.62.024502
    [6] 季顺迎, 李鹏飞, 陈晓东. 冲击荷载下颗粒物质缓冲性能的试验研究. 物理学报, 2012, 61(18): 184703. doi: 10.7498/aps.61.184703
    [7] 黄德财, 冯耀东, 解为梅, 陆明, 吴海平, 胡凤兰, 邓开明. 颗粒密度对旋转筒内二元颗粒体系分离的影响. 物理学报, 2012, 61(12): 124501. doi: 10.7498/aps.61.124501
    [8] 周志刚, 石玉仁, 刘丛波, 王光辉, 杨红娟. 非弹性蹦球的动力学研究. 物理学报, 2012, 61(20): 200501. doi: 10.7498/aps.61.200501
    [9] 郑鹤鹏, 蒋亦民, 彭政, 符力平. 颗粒固体弹性势能的声波性质. 物理学报, 2012, 61(21): 214502. doi: 10.7498/aps.61.214502
    [10] 毕忠伟, 孙其诚, 刘建国, 金峰, 张楚汉. 双轴压缩下颗粒物质剪切带的形成与发展. 物理学报, 2011, 60(3): 034502. doi: 10.7498/aps.60.034502
    [11] 姜泽辉, 郭波, 张峰, 王福力. 摩擦力对非弹性蹦球倍周期运动的影响. 物理学报, 2010, 59(12): 8444-8450. doi: 10.7498/aps.59.8444
    [12] 姜泽辉, 荆亚芳, 赵海发, 郑瑞华. 振动颗粒物质中倍周期运动对尺寸分离的影响. 物理学报, 2009, 58(9): 5923-5929. doi: 10.7498/aps.58.5923
    [13] 姜泽辉, 赵海发, 郑瑞华. 完全非弹性蹦球倍周期运动的分形特征. 物理学报, 2009, 58(11): 7579-7583. doi: 10.7498/aps.58.7579
    [14] 梁宣文, 李粮生, 侯兆国, 吕 震, 杨 雷, 孙 刚, 史庆藩. 垂直振动作用下二元混合颗粒分层的动态循环反转. 物理学报, 2008, 57(4): 2300-2305. doi: 10.7498/aps.57.2300
    [15] 郑鹤鹏, 蒋亦民. Couette颗粒系统中静态应力和侧压力系数的非线性弹性理论分析. 物理学报, 2008, 57(12): 7919-7927. doi: 10.7498/aps.57.7919
    [16] 张 航, 郭蕴博, 陈 骁, 王 端, 程鹏俊. 颗粒物质在冲击作用下的堆积分布. 物理学报, 2007, 56(4): 2030-2036. doi: 10.7498/aps.56.2030
    [17] 姜泽辉, 郑瑞华, 赵海发, 吴 晶. 完全非弹性蹦球的动力学行为. 物理学报, 2007, 56(7): 3727-3732. doi: 10.7498/aps.56.3727
    [18] 彭 政, 厚美瑛, 史庆藩, 陆坤权. 颗粒介质的离散态特性研究. 物理学报, 2007, 56(2): 1195-1202. doi: 10.7498/aps.56.1195
    [19] 李玉现, 刘建军, 李伯臧. 量子点接触中的电导与热功率:磁场与温度的影响. 物理学报, 2005, 54(3): 1366-1369. doi: 10.7498/aps.54.1366
    [20] 胡国琦, 张训生, 鲍德松, 唐孝威. 二维颗粒流通道宽度效应的分子动力学模拟. 物理学报, 2004, 53(12): 4277-4281. doi: 10.7498/aps.53.4277
计量
  • 文章访问数:  8861
  • PDF下载量:  306
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-06-23
  • 修回日期:  2017-12-15
  • 刊出日期:  2019-02-20

/

返回文章
返回