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Numerical Dynamics of Granular Materials

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Contact Mechanics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 103))

Abstract

Contact Dynamics is a numerical method, suitable for computing the dynamical motion of large collections of rigid bodies, with Coulomb friction taken into account in the event of contact. The principles of the method are sketched, in particular the way possible collisions or other nonsmooth features of the evolution are handled. As an example of application to granular dynamics, the construction of dry deposits and banks is simulated, in order to investigate their microstructure: force chains, geometrical anisotropy, Cauchy stress and some unexpected features of force transmission.

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References

  • Abadie, M. (2000) Dynamic simulation of rigid bodies: modelling of frictional contact, in Impacts in Mechanical Systems. Analysis and Modelling, edited by B. Brogliato, Springer-Verlag, Berlin Heidelberg, 61–144.

    Chapter  Google Scholar 

  • Alart, P., Curnier A. (1991) A mixed formulation for frictional contact problems prone to Newton like methods, Comput. Meth. in Appl. Mech. Engng. 92 353–375.

    Google Scholar 

  • Brogliato, B. (1999) Nonsmooth Mechanics, 2d. edition. Springer-Verlag, London.

    Google Scholar 

  • Brogliato, B., ten Dam, A. A., Paoli, L., Génot, F. and Abadie, M. (2001) Numerical simulation of finite dimensional multibody nonsmooth mechanical systems, ASME Applied Mechanics Reviews, to appear.

    Google Scholar 

  • Chabrand, P., Dubois, F., and Raous, M. (1998) Various numerical methods for solving unilateral contact problems with friction, Mathl. Comput. Modelling 28, 97108.

    Article  Google Scholar 

  • Christensen, P. W., Klarbring, A., Pang J. S., and Strömberg N. (1998) Formulation and comparison of algorithms for frictional contact problems, Int. J. Num. Meth. Engng. 42, 145–173.

    Article  MATH  Google Scholar 

  • Curnier, A. (1984) A theory of friction, Int. J. Solids Struct. 20, 637–647.

    Article  MATH  Google Scholar 

  • Daudon, D., Lanier, J., and Jean, M. (1997) A micromechanical comparison between experimental results and numerical simulation of a biaxial 2D granular material, in Powders and Grains 97, edited by R. P. Behringer and J. T. Jenkins, Balkema, Rotterdam, 219–222.

    Google Scholar 

  • Frémond, M. (1995) Rigid body collisions, Physics Letters A 204, 33–41.

    Article  MathSciNet  MATH  Google Scholar 

  • Génot, F., and Brogliato, B. (1999) New results on Painlevé paradoxes, European Journal of Mechanics, A/Solids, 18, 653–677.

    Article  MATH  Google Scholar 

  • Goddard, J. D. (1998) Continuum modelling of granular assemblies, in Physics of Dry Granular Materials, edited by H. J. Herrmann et al., Kluwer, Dordrecht Boston London, 1–24.

    Google Scholar 

  • Ivanov, A. P. (1997) The problem of constrained impact, J. Appl. Math. Mech. 61, 341–353.

    Article  Google Scholar 

  • Jean, M. (1999) The Non Smooth Contact Dynamics method, in Computational Modeling of Contact and Friction, edited by J. A. C. Martins and A. Klarbring, special issue of Computer Meth. in Appl. Mech. and Engng. 177, 235–257.

    Google Scholar 

  • Jean, M. (2001) Simulation numérique discrète de matériaux granulaires, in Micromécanique des matériaux granulaires, edited by B. Cambou and M. Jean, Hermes, Paris.

    Google Scholar 

  • Johansson, L., and Klarbring, A. (2000) Study of frictional impact using a nonsmooth equation solver, ASME J. Appl. Mech. 67, 267–273.

    Article  MATH  Google Scholar 

  • Jourdan, F., Alart, P., and Jean, M. (1998) A Gauss-Seidel-like algorithm to solve frictional contact problems. Computer Meth. Appl. Mech. Engng. 155, 31–47.

    Article  MathSciNet  MATH  Google Scholar 

  • Kunze, M., and Monteiro Marques, M. D. P. (2000) An introduction to Moreau’s sweeping process, in Impacts in Mechanical Systems. Analysis and Modelling, edited by B. Brogliato, Springer-Verlag, Berlin Heidelberg, 1–60.

    Chapter  Google Scholar 

  • Moreau, J. J. (1966) Quadratic programming in mechanics: dynamics of one-sided constraints, SIAM J. Control 4, 153–158.

    Article  MathSciNet  Google Scholar 

  • Moreau, J. J. (1988a) Bounded variation in time, in Topics in Nonsmooth Mechanics, edited by J. J. Moreau, P. D. Panagiotopoulos, and G. Strang, Birkhäuser, Basel Boston Berlin, 1–74.

    Google Scholar 

  • Moreau, J. J. (1988b) Unilateral contact and dry friction in finite freedom dynamics, in Nonsmooth Mechanics and Applications, edited by J. J. Moreau and P. D. Panagiotopoulos, CISM Courses and Lectures, Vol. 302. Springer-Verlag, Wien New York, 1–82.

    Google Scholar 

  • Moreau, J. J. (1989) An expression of classical dynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (suppl.), 1–48. Volume also available as Analyse Non Linéaire, edited by H. Attouch, J.-P. Aubin, F. Clarke, and I. Ekeland, Gauthier-Villars, Paris.

    Google Scholar 

  • Moreau J. J., (1997) Numerical investigation of shear zones in granular materials, in Proc. HLRZ-Workshop on Friction, Arching, Contact Dynamics, edited by P. Grassberger and D. Wolf, World Scientific, Singapore, 233–247.

    Google Scholar 

  • Moreau, J. J. (1999) Some basics of unilateral dynamics, in Unilateral Multibody Contacts, edited by F. Pfeiffer and Ch. Glocker, Kluwer, Dordrecht/Boston/London, 1–14.

    Chapter  Google Scholar 

  • Moreau J. J. (2000) Contact et frottement en dynamique des systèmes de corps rigides, Rev. Europ. des Eléments Finis 9, 9–28.

    MATH  Google Scholar 

  • Moreau J. J. (2001) An introduction to unilateral dynamics, in Novel approaches in Civil Engineering, edited by M. Frémond and F. Maceri, Springer-Verlag, to appear.

    Google Scholar 

  • Nouguier, C., Bohatier, C., Moreau, J. J., and Radjai, F. (2000) Force fluctuations in a pushed granular material, Granular matter 2, 171–178.

    Article  Google Scholar 

  • Pang, J. S., and Stewart, D. E. (1999) A unified approach to discrete frictional contact problems, Int. J. Engng. Sci., 37, 1747–1768.

    Article  MathSciNet  MATH  Google Scholar 

  • Pfeiffer F., and Glocker Ch. (1996) Multibody Dynamics with Unilateral Contacts, John Wiley and Sons, New York.

    Book  MATH  Google Scholar 

  • Stewart, D. E. (1998) Convergence of a time-stepping scheme for rigid body dynamics and resolution of Painlevé’s problem, Arch. Rational Mech. Anal. 145, 215–260.

    Article  MATH  Google Scholar 

  • Stoianovici, S. P., and Hurmuzlu, Y. (1996) A critical study of the concepts of rigid body collision theory, J. Appl. Mech. 63, 307–316.

    Article  Google Scholar 

  • Vola, D., Pratt, E., Jean, M., and Raous, M. (1998) Consistent time discretization for a dynamical frictional contact problem and complementarity techniques, Rev. Europ. des Eléments Finis 7, 149–162.

    MATH  Google Scholar 

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© 2002 Springer Science+Business Media Dordrecht

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Moreau, J.J. (2002). Numerical Dynamics of Granular Materials. In: Contact Mechanics. Solid Mechanics and Its Applications, vol 103. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1154-8_1

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  • DOI: https://doi.org/10.1007/978-94-017-1154-8_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6099-0

  • Online ISBN: 978-94-017-1154-8

  • eBook Packages: Springer Book Archive

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