The Spot Model for random-packing dynamics

Bazant, Martin Z.

doi:10.1016/j.mechmat.2005.06.016

The Spot Model for random-packing dynamics

Journal Article · Tue Aug 01 00:00:00 EDT 2006 · Mechanics of Materials

DOI:https://doi.org/10.1016/j.mechmat.2005.06.016· OSTI ID:882195

Bazant, Martin Z. ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); MIT

The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions or crystal-like vacancy diffusion, but here we propose a cooperative mechanism for dense random-packing dynamics, based on diffusing “spots” of interstitial free volume. Simulations with the Spot Model can efficiently generate realistic flowing packings, and yet the model is simple enough for mathematical analysis. Starting from a non-local stochastic differential equation, we derive continuum equations for tracer diffusion, given the dynamics of free volume (spots). Throughout the paper, we apply the model to granular drainage in a silo, and we also briefly discuss glassy relaxation. We conclude by discussing the prospects of spot-based multiscale modeling and simulation of amorphous materials.

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: FG02-02ER25530

OSTI ID:: 882195

Report Number(s):: DOE/ER/25530-2

Journal Information:: Mechanics of Materials, Journal Name: Mechanics of Materials Journal Issue: 8-10 Vol. 38; ISSN 0167-6636

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

References (39)

Confined granular packings: Structure, stress, and forces Landry, James W.; Grest, Gary S.; Silbert, Leonardo E. Physical Review E, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevE.67.041303	journal	April 2003
Stochastic Theory of Particle Flow under Gravity Mullins, W. W. Journal of Applied Physics, Vol. 43, Issue 2 https://doi.org/10.1063/1.1661175	journal	February 1972
Size segregation of granular matter in silo discharges Samadani, Azadeh; Pradhan, A.; Kudrolli, A. Physical Review E, Vol. 60, Issue 6 https://doi.org/10.1103/PhysRevE.60.7203	journal	December 1999
Origin of a Repose Angle: Kinetics of Rearrangement for Granular Materials Lemaître, Anaël Physical Review Letters, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevLett.89.064303	journal	July 2002
Compaction of granular mixtures: a free volume model Boutreux, T.; de Geennes, P. G. Physica A: Statistical Mechanics and its Applications, Vol. 244, Issue 1-4 https://doi.org/10.1016/S0378-4371(97)00236-7	journal	October 1997
Relaxation in glassforming liquids and amorphous solids Angell, C. A.; Ngai, K. L.; McKenna, G. B. Journal of Applied Physics, Vol. 88, Issue 6 https://doi.org/10.1063/1.1286035	journal	September 2000
On the Free‐Volume Model of the Liquid‐Glass Transition Turnbull, David; Cohen, Morrel H. The Journal of Chemical Physics, Vol. 52, Issue 6 https://doi.org/10.1063/1.1673434	journal	March 1970
Granular gravitational collapse and chute flow Ertaş, D.; Halsey, T. C. Europhysics Letters (EPL), Vol. 60, Issue 6 https://doi.org/10.1209/epl/i2002-00307-8	journal	December 2002
Improving the Density of Jammed Disordered Packings Using Ellipsoids Donev, A. Science, Vol. 303, Issue 5660 https://doi.org/10.1126/science.1093010	journal	February 2004
Geometric properties of random disk packings Lubachevsky, Boris D.; Stillinger, Frank H. Journal of Statistical Physics, Vol. 60, Issue 5-6 https://doi.org/10.1007/BF01025983	journal	September 1990
Diversity of order and densities in jammed hard-particle packings Kansal, Anuraag R.; Torquato, Salvatore; Stillinger, Frank H. Physical Review E, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevE.66.041109	journal	October 2002
Random loose packings of uniform spheres and the dilatancy onset Onoda, George Y.; Liniger, Eric G. Physical Review Letters, Vol. 64, Issue 22 https://doi.org/10.1103/PhysRevLett.64.2727	journal	May 1990
Plastic deformation in metallic glasses Argon, A. S. Acta Metallurgica, Vol. 27, Issue 1 https://doi.org/10.1016/0001-6160(79)90055-5	journal	January 1979
Local density fluctuations, hyperuniformity, and order metrics Torquato, Salvatore; Stillinger, Frank H. Physical Review E, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevE.68.041113	journal	October 2003
A stochastic model for continuum elasto-plastic behavior. I. Numerical approach and strain localization Bulatov, V. V.; Argon, A. S. Modelling and Simulation in Materials Science and Engineering, Vol. 2, Issue 2 https://doi.org/10.1088/0965-0393/2/2/001	journal	March 1994
A microscopic mechanism for steady state inhomogeneous flow in metallic glasses Spaepen, Frans Acta Metallurgica, Vol. 25, Issue 4 https://doi.org/10.1016/0001-6160(77)90232-2	journal	April 1977
On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids Adam, Gerold; Gibbs, Julian H. The Journal of Chemical Physics, Vol. 43, Issue 1 https://doi.org/10.1063/1.1696442	journal	July 1965
Granular solids, liquids, and gases Jaeger, Heinrich M.; Nagel, Sidney R.; Behringer, Robert P. Reviews of Modern Physics, Vol. 68, Issue 4 https://doi.org/10.1103/RevModPhys.68.1259	journal	October 1996
Jamming in hard sphere and disk packings Donev, Aleksandar; Torquato, Salvatore; Stillinger, Frank H. Journal of Applied Physics, Vol. 95, Issue 3 https://doi.org/10.1063/1.1633647	journal	February 2004
Multiplicity of Generation, Selection, and Classification Procedures for Jammed Hard-Particle Packings ^† Torquato, S.; Stillinger, F. H. The Journal of Physical Chemistry B, Vol. 105, Issue 47 https://doi.org/10.1021/jp011960q	journal	November 2001
Is Random Close Packing of Spheres Well Defined? Torquato, S.; Truskett, T. M.; Debenedetti, P. G. Physical Review Letters, Vol. 84, Issue 10, p. 2064-2067 https://doi.org/10.1103/PhysRevLett.84.2064	journal	March 2000
Pattern formation in flowing sand Baxter, G. William; Behringer, R. P.; Fagert, Timothy Physical Review Letters, Vol. 62, Issue 24 https://doi.org/10.1103/PhysRevLett.62.2825	journal	June 1989
Diffusion and Mixing in Gravity-Driven Dense Granular Flows Choi, Jaehyuk; Kudrolli, Arshad; Rosales, Rodolfo R. Physical Review Letters, Vol. 92, Issue 17 https://doi.org/10.1103/PhysRevLett.92.174301	journal	April 2004
Rearrangements and Dilatancy for Sheared Dense Materials Lemaître, Anaël Physical Review Letters, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevLett.89.195503	journal	October 2002
Velocity profile of granular flows inside silos and hoppers Choi, Jaehyuk; Kudrolli, Arshad; Bazant, Martin Z. Journal of Physics: Condensed Matter, Vol. 17, Issue 24 https://doi.org/10.1088/0953-8984/17/24/011	journal	June 2005
Statistical methods in the mechanics of granular bodies Litwiniszyn, J. Rheologica Acta, Vol. 1, Issue 2-3 https://doi.org/10.1007/BF01968857	journal	August 1958
Random-walk approach to granular flows Caram, H.; Hong, D. C. Physical Review Letters, Vol. 67, Issue 7 https://doi.org/10.1103/PhysRevLett.67.828	journal	August 1991
Dynamics of viscoplastic deformation in amorphous solids Falk, M. L.; Langer, J. S. Physical Review E, Vol. 57, Issue 6 https://doi.org/10.1103/PhysRevE.57.7192	journal	June 1998
Dynamics of random packings in granular flow Rycroft, Chris H.; Bazant, Martin Z.; Grest, Gary S. Physical Review E, Vol. 73, Issue 5 https://doi.org/10.1103/PhysRevE.73.051306	journal	May 2006
Relaxation processes in supercooled liquids Gotze, W.; Sjogren, L. Reports on Progress in Physics, Vol. 55, Issue 3 https://doi.org/10.1088/0034-4885/55/3/001	journal	March 1992
Jamming at zero temperature and zero applied stress: The epitome of disorder O’Hern, Corey S.; Silbert, Leonardo E.; Liu, Andrea J. Physical Review E, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevE.68.011306	journal	July 2003
Experimental evidence for the stochastic theory of particle flow under gravity Mullins, W. W. Powder Technology, Vol. 9, Issue 1 https://doi.org/10.1016/0032-5910(74)80006-9	journal	January 1974
Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates Eyring, Henry The Journal of Chemical Physics, Vol. 4, Issue 4 https://doi.org/10.1063/1.1749836	journal	April 1936
Random Packings of Frictionless Particles O'Hern, Corey S.; Langer, Stephen A.; Liu, Andrea J. Physical Review Letters, Vol. 88, Issue 7 https://doi.org/10.1103/PhysRevLett.88.075507	journal	January 2002
Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition Weeks, E. R. Science, Vol. 287, Issue 5453 https://doi.org/10.1126/science.287.5453.627	journal	January 2000
Molecular Transport in Liquids and Glasses Cohen, Morrel H.; Turnbull, David The Journal of Chemical Physics, Vol. 31, Issue 5 https://doi.org/10.1063/1.1730566	journal	November 1959
Statistical error in particle simulations of hydrodynamic phenomena Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.; Bazant, Martin Z. Journal of Computational Physics, Vol. 187, Issue 1 https://doi.org/10.1016/S0021-9991(03)00099-8	journal	May 2003
Stringlike Cooperative Motion in a Supercooled Liquid Donati, Claudio; Douglas, Jack F.; Kob, Walter Physical Review Letters, Vol. 80, Issue 11 https://doi.org/10.1103/PhysRevLett.80.2338	journal	March 1998
Experimental evidence supporting kinematic modelling of the flow of granular media in the absence of air drag Tüzün, U.; Nedderman, R. M. Powder Technology, Vol. 24, Issue 2 https://doi.org/10.1016/0032-5910(79)87044-8	journal	November 1979

Similar Records

Dynamics of random packings in granular flow

Journal Article · Wed May 24 00:00:00 EDT 2006 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics · OSTI ID:882197

Fast spot-based multiscale simulations of granular drainage

Journal Article · Fri May 22 00:00:00 EDT 2009 · Powder Technology · OSTI ID:960385

Related Subjects

36 MATERIALS SCIENCE
random packing
granular flow
multiscale simulation

The Spot Model for random-packing dynamics

Citation Formats

References (39)

Similar Records

Related Subjects