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On inconsistency in frictional granular systems

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Abstract

Numerical simulation of granular systems is often based on a discrete element method. The nonsmooth contact dynamics approach can be used to solve a broad range of granular problems, especially involving rigid bodies. However, difficulties could be encountered and hamper successful completion of some simulations. The slow convergence of the nonsmooth solver may sometimes be attributed to an ill-conditioned system, but the convergence may also fail. The prime aim of the present study was to identify situations that hamper the consistency of the mathematical problem to solve. Some simple granular systems were investigated in detail while reviewing and applying the related theoretical results. A practical alternative is briefly analyzed and tested.

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References

  1. Acary V, Brogliato B (2008) Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics. Springer, Berlin

    MATH  Google Scholar 

  2. Acary V, Cadoux F, Lemaréchal C, Malick J (2011) A formulation of the linear discrete Coulomb friction problem via convex optimization. Zeitschrift für angewandte Mathematik und Mechanik 91(2):155–175

    Article  MathSciNet  MATH  Google Scholar 

  3. Acary V, Cadoux F (2013) Applications of an existence result for the Coulomb friction problem. In: Recent advances in contact mechanics. Springer, Berlin, pp 45–66

  4. Alart P (2014) How to overcome indetermination and interpenetration in granular systems via nonsmooth contact dynamics. An exploratory investigation. Comput Methods Appl Mech Eng 270:37–56

    Article  MathSciNet  MATH  Google Scholar 

  5. Anderson JD, Wendt J (1995) Computational fluid dynamics, vol 206. Springer, Berlin

    Google Scholar 

  6. Avitzur B, Nakamura Y (1986) Analytical determination of friction resistance as a function of normal load and geometry of surface irregularities. Wear 107(4):367–383

    Article  Google Scholar 

  7. Azéma E, Radjai F, Saussine G (2009) Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech Mater 41(6):729–741

    Article  Google Scholar 

  8. Brogliato B (1999) Nonsmooth mechanics. Springer, Berlin

    Book  MATH  Google Scholar 

  9. Cantor D, Estrada N, Azéma E (2015) Split-cell method for grain fragmentation. Comput Geotech 67:150–156

    Article  Google Scholar 

  10. Champneys AR, Varkonyi PL (2016) The Painlevé paradox in contact mechanics. arXiv preprint arXiv:1601.03545

  11. Delassus E (1923) Sur les lois du frottement de glissement. Bulletin de la Société Mathématique de France 51:22–33

    Article  MathSciNet  MATH  Google Scholar 

  12. Dubois F, Jean M (2006) The non smooth contact dynamic method: recent LMGC90 software developments and application. In: Wriggers P, Nackenhorst U (eds) Analysis and simulation of contact problems. Springer, Berlin, pp 375–378

  13. Frémond M (2002) Non-smooth thermodynamics. Springer, Berlin

    MATH  Google Scholar 

  14. Frémond M (2007) Collisions. Dipartemento di Ingeneria Civile, Universitá di Roma Tor Vergata, Rome

    MATH  Google Scholar 

  15. Génot F, Brogliato B (1999) New results on Painlevé paradoxes. Eur J Mech A Solids 18(4):653–677

    Article  MathSciNet  MATH  Google Scholar 

  16. Jean M (1999) The non-smooth contact dynamics method. Comput Methods Appl Mech Eng 177:235–257

    Article  MathSciNet  MATH  Google Scholar 

  17. Klarbring A, Pang J-S (1998) Existence of solutions to discrete semicoercive frictional contact problems. SIAM J Optim 8(2):414–442

    Article  MathSciNet  MATH  Google Scholar 

  18. Koziara T, Bićanić N (2011) A distributed memory parallel multibody contact dynamics code. Int J Numer Methods Eng 87(1–5):437–456

    Article  MATH  Google Scholar 

  19. Laniel R, Alart P, Pagano S (2008) Discrete element investigations of wire-reinforced geomaterial in a three-dimensional modeling. Comput Mech 42(1):67–76

    Article  MATH  Google Scholar 

  20. Lecornu L (1905) Sur la loi de Coulomb. Comptes Rendus Acad Sci Paris 140:847–848

    MATH  Google Scholar 

  21. Moreau JJ (1999) Numerical aspects of sweeping process. Comput Methods Appl Mech Eng 177:329–349

    Article  MathSciNet  MATH  Google Scholar 

  22. Moreau JJ (2003) Modélisation et simulation de matériaux granulaires. In: Actes du 35eme Congres National dAnalyse Numérique

  23. Moreau JJ (2004) An introduction to unilateral dynamics. In: Fremond M, Maceri F (eds) Novel approaches in civil engineering. Lecture notes in applied and computational mechanics, vol 14. Springer, Berlin, pp 1–46

    Chapter  Google Scholar 

  24. Moreau JJ (2005) Indetermination in the numerical simulation of granular systems. In: Garcia-Rojo R, Herrmann HJ, Mc Namar S (eds) Powders and grains 2005. Balkema, Leiden, pp 109–112

    Google Scholar 

  25. Moreau JJ (2006) Facing the plurality of solutions in non smooth mechanics. In: Nonsmooth/nonconvex mechanics with applications in engineering. Proceeding international conference in memoriam of P.D. Panagiotopoulos. Editions Ziti, Thessaloniki, pp 3–12

  26. Nguyen NS, Brogliato B (2014) Multiple impacts in dissipative granular chains. Lecture notes in applied and computational mechanics, vol 72. Springer

  27. Nguyen D-H, Azéma E, Sornay P, Radjai F (2015) Bonded-cell model for particle fracture. Phys Rev E 91:022203

    Article  MathSciNet  Google Scholar 

  28. Orowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proc Inst Mech Eng 150(1):140–167

    Article  Google Scholar 

  29. Painlevé P (1905) Sur les lois de frottement et de glissement. Comptes Rendus Acad Sci Paris 121:112–115

    MATH  Google Scholar 

  30. Perales F, Dubois F, Monerie Y, Piar B, Stainier L (2010) A nonsmooth contact dynamics-based multi-domain solver: code coupling (Xper) and application to fracture. Eur J Comput Mech /Revue Européenne de Mécanique Numérique 19(4):389–417

    Article  Google Scholar 

  31. Radjaï F, Jean M, Moreau JJ, Roux S (1996) Force distributions in dense two dimensional granular systems. Phys Rev Lett 77:274–277

    Article  Google Scholar 

  32. Radjaï F, Wolf DE, Jean M, Moreau JJ (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61–64

    Article  Google Scholar 

  33. Renouf M, Alart P (2005) Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials. Comput Methods Appl Mech Eng 194(18–20):2019–2041

    Article  MathSciNet  MATH  Google Scholar 

  34. Renouf M, Dubois F, Alart P (2006) Numerical investigations of fault propagation and forced-fold using a non smooth discrete element method. Eur J Comput Mech 15:549–570

    Article  MATH  Google Scholar 

  35. Stupkiewicz S, Mróz Z (1999) A model of third body abrasive friction and wear in hot metal forming. Wear 231(1):124–138

    Article  Google Scholar 

  36. Visseq V, Martin A, Iceta D, Azema E, Dureisseix D, Alart P (2012) Dense granular dynamics analysis by a domain decomposition approach. Comput Mech 49:709–723

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. LMGC, Université de Montpellier, CNRS, Montpellier, France

    Pierre Alart & Mathieu Renouf

  2. Laboratoire de Micromécanique et d’Intégrité des Structures (MIST), IRSN, Université de Montpellier, CNRS, Montpellier, France

    Pierre Alart

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  1. Pierre Alart
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  2. Mathieu Renouf
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Correspondence to Pierre Alart.

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Alart, P., Renouf, M. On inconsistency in frictional granular systems. Comp. Part. Mech. 5, 161–174 (2018). https://doi.org/10.1007/s40571-017-0160-9

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  • DOI: https://doi.org/10.1007/s40571-017-0160-9

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