For investigating the mechanical behavior of granular materials by means of the discrete element approach, it is desirable to be able to simulate representative volume elements with macroscopically homogeneous deformations. This can be achieved by means of fully periodic boundary conditions such that stresses or displacements can be applied in all space directions. We present a general framework for periodic boundary conditions in granular materials and its implementation more specifically in the Contact Dynamics method.
Accepté le :
Publié le :
@article{CRMECA_2018__346_3_263_0,
author = {Farhang Radjai},
title = {Multi-periodic boundary conditions and the {Contact} {Dynamics} method},
journal = {Comptes Rendus. M\'ecanique},
pages = {263--277},
publisher = {Elsevier},
volume = {346},
number = {3},
year = {2018},
doi = {10.1016/j.crme.2017.12.007},
language = {en},
}
Farhang Radjai. Multi-periodic boundary conditions and the Contact Dynamics method. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 263-277. doi : 10.1016/j.crme.2017.12.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.007/
[1] A discrete numerical model for granular assemblies, Géotechnique, Volume 29 (1979) no. 1, pp. 47-65
[2] Impact of elastic spheres with and without adhesion, Powder Technol., Volume 65 (1991), p. 153
[3] Molecular dynamics simulations of dry granular media, Osaka, Japan (1993), p. 8
[4] Computer simulation of impact fracture/fragmentation, Osaka, Japan (1993), p. 17
[5] Molecular dynamics of arbitrarily shaped granular particles, J. Phys. I France, Volume 5 (1995) no. 11, pp. 1431-1455
[6] Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres, J. Appl. Mech., Volume 64 (1997), pp. 383-386
[7] Collisions and contacts between two particles (H.J. Herrmann; J.-P. Hovi; S. Luding, eds.), Physics of Dry Granular Media, NATO ASI Ser., vol. E350, Kluwer Academic Publishers, Dordrecht, 1998, p. 285
[8] Discrete element methods for the simulation of dense packings and heaps made of spherical and non-spherical particles, Powder Technol., Volume 109 (2000), pp. 278-292
[9] Measurement of indeterminacy in packings of perfectly rigid disks, Phys. Rev. E, Volume 70 (2004) no. 6 Pt 1
[10] Acoustic response of cemented granular sedimentary rocks: molecular dynamics modeling, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 75 (2007) no. 6 Pt 1
[11] Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states, Phys. Rev. E, Volume 75 (2007) no. 1 Pt 1
[12] Stress transmission in wet granular materials, Eur. Phys. J. E, Volume 21 (2007), pp. 359-369
[13] Evolution problem associated with a moving convex set in a Hilbert space, J. Differ. Equ., Volume 26 (1977), pp. 347-374
[14] Liaisons unilatérales sans frottement et chocs inélastiques, C. R. Acad. Sci. Paris, Ser. II, Volume 296 (1983), pp. 1473-1476
[15] Bounded variation in time (P. Panagiotopoulos; G. Strang, eds.), Topics in Nonsmooth Mechanics, Bikhäuser, Basel, Switzerland, 1988, pp. 1-74
[16] Unilateral contact and dry friction in finite freedom dynamics, Nonsmooth Mechanics and Applications, International Centre for Mechanical Sciences, Courses and Lectures, vol. 302, Springer, Vienna, 1988, pp. 1-82
[17] New computation methods in granular dynamics, Powders & Grains 93, A. A. Balkema, Rotterdam, The Netherlands, 1993, p. 227
[18] Some numerical methods in multibody dynamics: application to granular, Eur. J. Mech. A, Solids, Volume 13 (1994), pp. 93-114
[19] A system of rigid bodies with dry friction, Int. J. Eng. Sci. (1985), pp. 497-513
[20] Unilateral contact and dry friction: time and space variables discretization, Arch. Mech. Warszawa, Volume 40 (1988) no. 1, pp. 677-691
[21] Unilaterality and dry friction in the dynamics of rigid body collections, Proceedings of Contact Mechanics International Symposium, Presses polytechniques et universitaires romandes, Lausanne, Switzerland, 1992, pp. 31-48
[22] Numerical investigation of shear zones in granular materials (D.E. Wolf; P. Grassberger, eds.), Friction, Arching, Contact Dynamics, World Scientific, Singapore, 1997, pp. 233-247
[23] Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett., Volume 77 (1996) no. 2, p. 274
[24] Bimodal character of stress transmission in granular packings, Phys. Rev. Lett., Volume 80 (1998), pp. 61-64
[25] Dynamic rearrangements and packing regimes in randomly deposited two-dimensional granular beds, Phys. Rev. E, Volume 66 (2002)
[26] Turbulentlike fluctuations in quasistatic flow of granular media, Phys. Rev. Lett., Volume 89 (2002) no. 6
[27] Preavalanche instabilities in a granular pile, Phys. Rev. Lett., Volume 89 (2002)
[28] Influence of particle shape and angularity on the behavior of granular materials: a numerical analysis, Int. J. Numer. Anal. Methods Geomech., Volume 27 (2003), pp. 1207-1226
[29] A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media, J. Comput. Appl. Math., Volume 168 (2004) no. 1–2, pp. 375-382
[30] Rheology, force transmission, and shear instabilities in frictional granular media from biaxial numerical test using the contact dynamics method, J. Geophys. Res., Volume 110 (2005), pp. 1-24
[31] Modelling ballast behaviour under dynamic loading. Part 1: a 2d polygonal discrete element method approach, Comput. Methods Appl. Mech. Eng., Volume 195 (2006) no. 19–22, pp. 2841-2859
[32] Force transmission in a packing of pentagonal particles, Phys. Rev. E, Volume 76 (2007) no. 1 Pt 1
[33] Shear zones in granular media: three-dimensional contact dynamics simulation, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 76 (2007) no. 5 Pt 1
[34] Numerical simulation of monuments by the contact dynamics method (DGEMN-LNEC-JRC, ed.), Monument-98, Workshop on Seismic Performance of Monuments, LNEC, 1998, pp. 12-14
[35] Approche multi-échelle des systèmes de tenségrité, Rev. Eur. Méc. Numér., Volume 15 (2006), pp. 319-328
[36] Stick-slip dynamics of a one-dimensional array of particles, Phys. Rev. E, Volume 52 (1995) no. 5, pp. 5555-5564
[37] Collective friction of an array of particles: a crucial test for numerical algorithms, J. Phys. I France, Volume 7 (1997), p. 1053
[38] Multicontact dynamics of granular systems, Comput. Phys. Commun., Volume 121–122 (1999), pp. 294-298
[39] Experiments and numerical simulations with 2d disks assembly, Powder Technol., Volume 109 (2000), pp. 206-221
[40] Contact dynamics study of 2d granular media: critical states and relevant internal variables (H. Hinrichsen; D.E. Wolf, eds.), The Physics of Granular Media, Wiley-VCH, Weinheim, Germany, 2004, pp. 165-186
[41] Quasirigidity: some uniqueness issues, Phys. Rev. E, Volume 74 (2006) no. 6 Pt 1
[42] A DEM comparison of different shear testing devices (Y. Kishino, ed.), Powders and Grains 2001, A.A. Balkema, 2001, pp. 183-190
[43] Computer Simulation of Liquids, Oxford University Press, Oxford, UK, 1987
[44] Crystal structure and pair potentials: a molecular-dynamics study, Phys. Rev. Lett., Volume 45 (1980), p. 1196
[45] An introduction to unilateral dynamics (M. Frémond; F. Maceri, eds.), Novel Approaches in Civil Engineering, Lect. Notes Appl. Comput. Mech., vol. 14, Springer-Verlag, 2004, pp. 1-46
[46] Contact dynamics as a nonsmooth discrete element method, M. Mater., Volume 41 (2009), pp. 715-728
[47] Constant-temperature–constant pressure molecular-dynamics calculations for molecular solids: application to solid nitrogen at high pressure, Phys. Rev. B, Volume 33 (1986), pp. 339-342
[48] Metric tensor as the dynamical variable for variable-cell-shape molecular dynamics, Phys. Rev. B, Volume 55 (1997), pp. 8733-8742
[49] Solid-like behavior and anisotropy in rigid frictionless bead assemblies, Phys. Rev. E, Volume 78 (2008)
[50] Frictionless bead packs have macroscopic friction, but no dilatancy, Phys. Rev. E, Volume 78 (2008)
[51] Polymorphic transitions in single crystals: a new molecular dynamics method, J. Appl. Phys., Volume 52 (1981), p. 7182
[52] A framework for micromacro transitions in periodic particle aggregates of granular materials, Comput. Methods Appl. Mech. Eng., Volume 193 (2004), pp. 225-256
[53] On (Andersen–)Parrinello–Rahman molecular dynamics, the related metadynamics, and the use of the Cauchy–Born rule, J. Elast., Volume 100 (2010), pp. 145-153
[54] The stress tensor in a granular flow at high shear rates, J. Fluid Mech., Volume 110 (1981), p. 255
[55] Computer simulations and experiment on the quasistatic mechanics and transport properties of granular materials (E. Guazzelli; L. Oger, eds.), Mobile Particulate Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995, p. 261
[56] Microstructural stress tensor of granular assemblies with volume forces, J. Appl. Mech., Volume 66 (1999) no. 4, pp. 934-936
[57] Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 76 (2007) no. 6–1
[58] Internal states of model isotropic granular packings. II. Compression and pressure cycles, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 76 (2007) no. 6–1
Cité par Sources :
Commentaires - Politique
Richard L. Weaver
C. R. Géos (2011)
Snowpack permittivity profile retrieval from tomographic SAR data
Badreddine Rekioua; Matthieu Davy; Laurent Ferro-Famil; ...
C. R. Phys (2017)