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Discrete element analysis of buffering capacity of non-spherical granular materials based on super-quadric method

Wang Si-Qiang Ji Shun-Ying

Discrete element analysis of buffering capacity of non-spherical granular materials based on super-quadric method

Wang Si-Qiang, Ji Shun-Ying
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  • Granular system commonly encountered in industry or nature is comprised of non-spherical grains. Comparing with spherical particles, high discretization and interlocking among non-spherical particles can effectively dissipate the system energy and improve the buffer capacity. The superquadric element based on continuous function envelop can form the geometric shape of irregular particles accurately, and then contact collision action between particles can be calculated easily. In this paper, we provide a comprehensive introduction to particle-particle and particle-boundary contact collision. In addition, considering different shapes and surface curvatures under various contact patterns between super-quadric particles, the linear contact force model cannot be applied to the accurate calculation of the contact force, and a corresponding non-linear viscoelastic force model is developed. In this model, the equivalent radius of curvature at a local contact point is adopted to calculate the normal contact force, and the tangential contact force is simplified based on the contact model of spherical elements. To examine the validity of the algorithm and this model, we compare the discrete element analytical results with the analytical results for a single cylinder impacting a flat wall and the previous experimental results for spherical granular material under impact load, and this method is verified by good agreement between the simulated results and the previous experimental results. According to the aforementioned method, we study the buffer capacity of non-spherical particles under impact load by the discrete element method, and the influences of granular thickness and particle shapes on the buffer capacity are discussed. The results show that a critical thickness Hc is obtained for different particle shapes. The buffer capacity is improved with increasing the granular thickness when H Hc, but is independent of the granular thickness and particle shapes when H Hc. Moreover, the impact peak and initial packing fraction increase significantly with increasing the blockiness. Rectangular particles account for the highest packing fraction, and the packing fraction of cylindrical particles is higher than the packing fraction of spherical particles. Therefore, Rectangular particles are more likely to form dense face-face contacts and ordered packing structures with high packing fraction. These denser packings prevent the particles from their relatively moving, and thus reducing the buffering capacity of the particles. Furthermore, the impact peak and initial packing fraction decrease with increasing or reducing the aspect ratio of cylindrical particles and the aspect ratio of rectangular particles. The aspect ratio of particle can be used to adjust the dense packing structure and reduce the stability of the system. It means that the particles have more effective buffer capacity for the non-spherical particle system.
      Corresponding author: Ji Shun-Ying, jisy@dlut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11572067, 11772085).
    [1]

    Katsuragi H, Durian D J 2007 Nat. Phys. 3 420

    [2]

    Kondic L, Fang X, Losert W, OHern C S, Behringer R P 2012 Phys. Rev. E 85 011305

    [3]

    Nordstrom K, Lim E, Harrington M, Losert W 2014 Phys. Rev. Lett. 112 228002

    [4]

    Bester C S, Behringer R P 2017 Phys. Rev. E 95 032906

    [5]

    Seguin A, Bertho Y, Gondret P, Crassous J 2009 Europhys. Lett. 88 44002

    [6]

    Clark A H, Petersen A J, Kondic L, Behringer R P 2015 Phys. Rev. Lett. 114 144502

    [7]

    Deboeuf S, Gondret P, Rabaud M 2008 Environ. Sci. Technol. 42 8459

    [8]

    Deboeuf S, Gondret P, Rabaud M 2009 Phys. Rev. E 79 041306

    [9]

    Ye X Y, Wang D M, Zheng X J 2012 Phys. Rev. E 86 061304

    [10]

    Lu G, Third J R, Mller C R 2015 Chem. Eng. Sci. 127 425

    [11]

    Zhong W, Yu A, Liu X, Tong Z, Zhang H 2016 Powder Technol. 302 108

    [12]

    Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2007 Chem. Eng. Sci. 62 3378

    [13]

    Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2008 Chem. Eng. Sci. 63 5728

    [14]

    Elskamp F, Kruggel-Emden H, Hennig M, Teipel U 2017 Granular Matter 19 46

    [15]

    Zhao S, Zhang N, Zhou X, Zhang L 2017 Powder Technol. 310 175

    [16]

    Kruggel-Emden H, Rickelt S, Wirtz S, Scherer V 2008 Powder Technol. 188 153

    [17]

    Li C Q, Xu W J, Meng Q S 2015 Powder Technol. 286 478

    [18]

    Zeng Y, Jia F, Zhang Y, Meng X, Han Y, Wang H 2017 Powder Technol. 313 112

    [19]

    Galindo-Torres S A, Pedroso D M 2010 Phys. Rev. E 81 061303

    [20]

    Toson P, Khinast J G 2017 Powder Technol. 313 353

    [21]

    Govender N, Wilke D N, Pizette P, Abriak N E 2018 Appl. Math. Comput. 319 318

    [22]

    Lu G, Third J R, Mller C R 2012 Chem. Eng. Sci. 78 226

    [23]

    Cui Z Q, Chen Y C, Zhao Y Z, Hua Z L, Liu X, Zhou C L 2013 Chin. J. Computat. Mech. 30 854 (in Chinese) [崔泽群, 陈友川, 赵永志, 花争立, 刘骁, 周池楼 2013 计算力学学报 30 854]

    [24]

    Cleary P W, Sinnott M D, Morrison R D, Cummins S, Delaney G W 2017 Miner. Eng. 100 49

    [25]

    Di Renzo A, Di Maio F P 2004 Chem. Eng. Sci. 59 525

    [26]

    Liu S D, Zhou Z Y, Zou R P, Pinson D, Yu A B 2014 Powder Technol. 253 70

    [27]

    Goldman D I, Umbanhowar P 2008 Phys. Rev. E 77 021308

    [28]

    Vet S J D, Bruyn J R D 2012 Granular Matter 14 661

    [29]

    Clark A H, Petersen A J, Behringer R P 2014 Phys. Rev. E 89 012201

    [30]

    Clark A H, Kondic L, Behringer R P 2016 Phys. Rev. E 93 050901

    [31]

    Ji S Y, Li P F, Chen X D 2012 Acta Phys. Sin. 61 184703 (in Chinese) [季顺迎, 李鹏飞, 陈晓东 2012 物理学报 61 184703]

    [32]

    Ji S Y, Fan L F, Liang S M 2016 Acta Phys. Sin. 65 104501 (in Chinese) [季顺迎, 樊利芳, 梁绍敏 2016 物理学报 65 104501]

    [33]

    Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667 (in Chinese) [孙其诚, 王光谦 2008 物理学报 57 4667]

    [34]

    Peng Z, Jiang Y M, Liu R, Hou M Y 2013 Acta Phys. Sin. 62 024502 (in Chinese) [彭政, 蒋亦民, 刘锐, 厚美瑛 2013 物理学报 62 024502]

    [35]

    Barr A H 1981 IEEE Comput. Graph. Appl. 1 11

    [36]

    Stenzel O, Salzer M, Schmidt V, Cleary P W, Delaney G W 2014 Granular Matter 16 457

    [37]

    Delaney G W, Cleary P W 2010 Europhys. Lett. 89 34002

    [38]

    Portal R, Dias J, de Sousa L 2010 Arch. Mech. Eng. 57 165

    [39]

    Wellmann C, Lillie C, Wriggers P 2008 Eng. Computat. 25 432

    [40]

    Podlozhnyuk A, Pirker S, Kloss C 2017 Comp. Part. Mech. 4 101

    [41]

    Goldman R 2005 Comput. Aided Geomet. Desig. 22 632

    [42]

    Gan J Q, Zhou Z Y, Yu A B 2017 Powder Technol. 320 610

    [43]

    Kremmer M, Favier J F 2001 Int. J. Numer. Meth. Eng. 51 1407

    [44]

    Kodam M, Bharadwaj R, Curtis J, Hancock B, Wassgren C 2010 Chem. Eng. Sci. 65 5863

  • [1]

    Katsuragi H, Durian D J 2007 Nat. Phys. 3 420

    [2]

    Kondic L, Fang X, Losert W, OHern C S, Behringer R P 2012 Phys. Rev. E 85 011305

    [3]

    Nordstrom K, Lim E, Harrington M, Losert W 2014 Phys. Rev. Lett. 112 228002

    [4]

    Bester C S, Behringer R P 2017 Phys. Rev. E 95 032906

    [5]

    Seguin A, Bertho Y, Gondret P, Crassous J 2009 Europhys. Lett. 88 44002

    [6]

    Clark A H, Petersen A J, Kondic L, Behringer R P 2015 Phys. Rev. Lett. 114 144502

    [7]

    Deboeuf S, Gondret P, Rabaud M 2008 Environ. Sci. Technol. 42 8459

    [8]

    Deboeuf S, Gondret P, Rabaud M 2009 Phys. Rev. E 79 041306

    [9]

    Ye X Y, Wang D M, Zheng X J 2012 Phys. Rev. E 86 061304

    [10]

    Lu G, Third J R, Mller C R 2015 Chem. Eng. Sci. 127 425

    [11]

    Zhong W, Yu A, Liu X, Tong Z, Zhang H 2016 Powder Technol. 302 108

    [12]

    Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2007 Chem. Eng. Sci. 62 3378

    [13]

    Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2008 Chem. Eng. Sci. 63 5728

    [14]

    Elskamp F, Kruggel-Emden H, Hennig M, Teipel U 2017 Granular Matter 19 46

    [15]

    Zhao S, Zhang N, Zhou X, Zhang L 2017 Powder Technol. 310 175

    [16]

    Kruggel-Emden H, Rickelt S, Wirtz S, Scherer V 2008 Powder Technol. 188 153

    [17]

    Li C Q, Xu W J, Meng Q S 2015 Powder Technol. 286 478

    [18]

    Zeng Y, Jia F, Zhang Y, Meng X, Han Y, Wang H 2017 Powder Technol. 313 112

    [19]

    Galindo-Torres S A, Pedroso D M 2010 Phys. Rev. E 81 061303

    [20]

    Toson P, Khinast J G 2017 Powder Technol. 313 353

    [21]

    Govender N, Wilke D N, Pizette P, Abriak N E 2018 Appl. Math. Comput. 319 318

    [22]

    Lu G, Third J R, Mller C R 2012 Chem. Eng. Sci. 78 226

    [23]

    Cui Z Q, Chen Y C, Zhao Y Z, Hua Z L, Liu X, Zhou C L 2013 Chin. J. Computat. Mech. 30 854 (in Chinese) [崔泽群, 陈友川, 赵永志, 花争立, 刘骁, 周池楼 2013 计算力学学报 30 854]

    [24]

    Cleary P W, Sinnott M D, Morrison R D, Cummins S, Delaney G W 2017 Miner. Eng. 100 49

    [25]

    Di Renzo A, Di Maio F P 2004 Chem. Eng. Sci. 59 525

    [26]

    Liu S D, Zhou Z Y, Zou R P, Pinson D, Yu A B 2014 Powder Technol. 253 70

    [27]

    Goldman D I, Umbanhowar P 2008 Phys. Rev. E 77 021308

    [28]

    Vet S J D, Bruyn J R D 2012 Granular Matter 14 661

    [29]

    Clark A H, Petersen A J, Behringer R P 2014 Phys. Rev. E 89 012201

    [30]

    Clark A H, Kondic L, Behringer R P 2016 Phys. Rev. E 93 050901

    [31]

    Ji S Y, Li P F, Chen X D 2012 Acta Phys. Sin. 61 184703 (in Chinese) [季顺迎, 李鹏飞, 陈晓东 2012 物理学报 61 184703]

    [32]

    Ji S Y, Fan L F, Liang S M 2016 Acta Phys. Sin. 65 104501 (in Chinese) [季顺迎, 樊利芳, 梁绍敏 2016 物理学报 65 104501]

    [33]

    Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667 (in Chinese) [孙其诚, 王光谦 2008 物理学报 57 4667]

    [34]

    Peng Z, Jiang Y M, Liu R, Hou M Y 2013 Acta Phys. Sin. 62 024502 (in Chinese) [彭政, 蒋亦民, 刘锐, 厚美瑛 2013 物理学报 62 024502]

    [35]

    Barr A H 1981 IEEE Comput. Graph. Appl. 1 11

    [36]

    Stenzel O, Salzer M, Schmidt V, Cleary P W, Delaney G W 2014 Granular Matter 16 457

    [37]

    Delaney G W, Cleary P W 2010 Europhys. Lett. 89 34002

    [38]

    Portal R, Dias J, de Sousa L 2010 Arch. Mech. Eng. 57 165

    [39]

    Wellmann C, Lillie C, Wriggers P 2008 Eng. Computat. 25 432

    [40]

    Podlozhnyuk A, Pirker S, Kloss C 2017 Comp. Part. Mech. 4 101

    [41]

    Goldman R 2005 Comput. Aided Geomet. Desig. 22 632

    [42]

    Gan J Q, Zhou Z Y, Yu A B 2017 Powder Technol. 320 610

    [43]

    Kremmer M, Favier J F 2001 Int. J. Numer. Meth. Eng. 51 1407

    [44]

    Kodam M, Bharadwaj R, Curtis J, Hancock B, Wassgren C 2010 Chem. Eng. Sci. 65 5863

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  • Received Date:  29 November 2017
  • Accepted Date:  20 January 2018
  • Published Online:  05 May 2018

Discrete element analysis of buffering capacity of non-spherical granular materials based on super-quadric method

    Corresponding author: Ji Shun-Ying, jisy@dlut.edu.cn
  • 1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11572067, 11772085).

Abstract: Granular system commonly encountered in industry or nature is comprised of non-spherical grains. Comparing with spherical particles, high discretization and interlocking among non-spherical particles can effectively dissipate the system energy and improve the buffer capacity. The superquadric element based on continuous function envelop can form the geometric shape of irregular particles accurately, and then contact collision action between particles can be calculated easily. In this paper, we provide a comprehensive introduction to particle-particle and particle-boundary contact collision. In addition, considering different shapes and surface curvatures under various contact patterns between super-quadric particles, the linear contact force model cannot be applied to the accurate calculation of the contact force, and a corresponding non-linear viscoelastic force model is developed. In this model, the equivalent radius of curvature at a local contact point is adopted to calculate the normal contact force, and the tangential contact force is simplified based on the contact model of spherical elements. To examine the validity of the algorithm and this model, we compare the discrete element analytical results with the analytical results for a single cylinder impacting a flat wall and the previous experimental results for spherical granular material under impact load, and this method is verified by good agreement between the simulated results and the previous experimental results. According to the aforementioned method, we study the buffer capacity of non-spherical particles under impact load by the discrete element method, and the influences of granular thickness and particle shapes on the buffer capacity are discussed. The results show that a critical thickness Hc is obtained for different particle shapes. The buffer capacity is improved with increasing the granular thickness when H Hc, but is independent of the granular thickness and particle shapes when H Hc. Moreover, the impact peak and initial packing fraction increase significantly with increasing the blockiness. Rectangular particles account for the highest packing fraction, and the packing fraction of cylindrical particles is higher than the packing fraction of spherical particles. Therefore, Rectangular particles are more likely to form dense face-face contacts and ordered packing structures with high packing fraction. These denser packings prevent the particles from their relatively moving, and thus reducing the buffering capacity of the particles. Furthermore, the impact peak and initial packing fraction decrease with increasing or reducing the aspect ratio of cylindrical particles and the aspect ratio of rectangular particles. The aspect ratio of particle can be used to adjust the dense packing structure and reduce the stability of the system. It means that the particles have more effective buffer capacity for the non-spherical particle system.

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