Effect of shape and friction on the packing and flow of granular materials

Salerno, K. Michael; Bolintineanu, Dan S.; Grest, Gary S.; Lechman, Jeremy B.; Plimpton, Steven J.; Srivastava, Ishan; Silbert, Leonardo E.

doi:10.1103/PhysRevE.98.050901

Title: Effect of shape and friction on the packing and flow of granular materials

Journal Article · 06 November 2018 · Physical Review E

DOI: https://doi.org/10.1103/PhysRevE.98.050901 · OSTI ID:1483965

Salerno, K. Michael ^[1]; Bolintineanu, Dan S. ^[2]; Grest, Gary S. ^[2]; Lechman, Jeremy B. ^[2]; Plimpton, Steven J. ^[2]; Srivastava, Ishan ^[2]; Silbert, Leonardo E. ^[3]

Army Research Lab., MD (United States). Aberdeen Proving Ground
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Central New Mexico Community College, Albuquerque, NM (United States). School of Math, Science, and Engineering

Here, the packing and flow of aspherical frictional particles are studied using discrete element simulations. Particles are superballs with shape |x|^s + |y|^s + |z|^s = 1 that varies from sphere (s = 2) to cube (s = ∞), constructed with an overlapping-sphere model. Both packing fraction, Φ, and coordination number, z, decrease monotonically with microscopic friction μ, for all shapes. However, this decrease is more dramatic for larger s due to a reduction in the fraction of face-face contacts with increasing friction. For flowing grains, the dynamic friction ~μ —the ratio of shear to normal stresses—depends on shape, microscopic friction, and inertial number I . For all shapes, ˜μ grows from its quasistatic value ˜μ₀ as (˜μ - ˜μ₀) = dI^α, with different universal behavior for frictional and frictionless shapes. For frictionless shapes the exponent α ≈ 0.5 and prefactor d ≈ 5˜μ₀ while for frictional shapes α ≈ 1 and d varies only slightly. Lastly, the results highlight that the flow exponents are universal and are consistent for all the shapes simulated here.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1483965

Alternate ID(s):: OSTI ID: 1481230; OSTI ID: 1485843

Report Number(s):: SAND--2018-2025J; 662902

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 98; ISSN PLEEE8; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (85)

Effect of particle shape on the density and microstructure of random packings Wouterse, Alan; Williams, Stephen R.; Philipse, Albert P. Journal of Physics: Condensed Matter, Vol. 19, Issue 40 https://doi.org/10.1088/0953-8984/19/40/406215	journal	September 2007
A first-order phase transition defines the random close packing of hard spheres Jin, Yuliang; Makse, Hernán A. Physica A: Statistical Mechanics and its Applications, Vol. 389, Issue 23 https://doi.org/10.1016/j.physa.2010.08.010	journal	December 2010
Evaluation of the packing characteristics of mono-sized non-spherical particles Zou, R. P.; Yu, A. B. Powder Technology, Vol. 88, Issue 1 https://doi.org/10.1016/0032-5910(96)03106-3	journal	July 1996
Maximum and minimum stable random packings of Platonic solids Baker, Jessica; Kudrolli, Arshad Physical Review E, Vol. 82, Issue 6 https://doi.org/10.1103/PhysRevE.82.061304	journal	December 2010
Particle Shape Effects on the Stress Response of Granular Packings Athanassiadis, Athanasios G.; Miskin, Marc Z.; Kaplan, Paul arXiv https://doi.org/10.48550/arxiv.1308.2241	text	January 2013
Variations in shear behavior among specimens with different packing patterns Katagiri, Jun; Matsushima, Takashi; Yamada, Yasuo Granular Matter, Vol. 16, Issue 6 https://doi.org/10.1007/s10035-014-0530-4	journal	October 2014
Particle shape effects on fabric of granular random packing Zhao, Shiwei; Zhang, Nan; Zhou, Xiaowen Powder Technology, Vol. 310 https://doi.org/10.1016/j.powtec.2016.12.094	journal	April 2017
Interplay of particle shape and suspension properties: a study of cube-like particles Audus, Debra J.; Hassan, Ahmed M.; Garboczi, Edward J. Soft Matter, Vol. 11, Issue 17 https://doi.org/10.1039/C4SM02869D	journal	January 2015
Phase Diagram for Inertial Granular Flows DeGiuli, E.; McElwaine, J. N.; Wyart, M. arXiv https://doi.org/10.48550/arxiv.1509.03512	text	January 2015
Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles Azéma, E.; Radjai, F.; Saussine, G. Mechanics of Materials, Vol. 41, Issue 6 https://doi.org/10.1016/j.mechmat.2009.01.021	journal	June 2009
Phase Behavior of Colloidal Superballs: Shape Interpolation from Spheres to Cubes Batten, Robert D.; Stillinger, Frank H.; Torquato, Salvatore arXiv https://doi.org/10.48550/arxiv.1005.0534	text	January 2010
Maximally dense random packings of spherocylinders Meng, Lingyi; Jiao, Yang; Li, Shuixiang Powder Technology, Vol. 292 https://doi.org/10.1016/j.powtec.2016.01.036	journal	May 2016
Discrete simulation of dense flows of polyhedral grains down a rough inclined plane Azéma, Emilien; Descantes, Yannick; Roquet, Nicolas Physical Review E, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevE.86.031303	journal	September 2012
Variable-cell method for stress-controlled jamming of athermal, frictionless grains Smith, Kyle C.; Srivastava, Ishan; Fisher, Timothy S. Physical Review E, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevE.89.042203	journal	April 2014
Granular materials composed of shape-anisotropic grains Börzsönyi, Tamás; Stannarius, Ralf Soft Matter, Vol. 9, Issue 31 https://doi.org/10.1039/c3sm50298h	journal	January 2013
Rheology of cubic particles suspended in a Newtonian fluid Cwalina, Colin D.; Harrison, Kelsey J.; Wagner, Norman J. Soft Matter, Vol. 12, Issue 20 https://doi.org/10.1039/C6SM00205F	journal	January 2016
Particle shape effects on the stress response of granular packings Athanassiadis, Athanasios G.; Miskin, Marc Z.; Kaplan, Paul Soft Matter, Vol. 10, Issue 1 https://doi.org/10.1039/C3SM52047A	journal	January 2014
A composite particle model for non-spherical particles in DEM simulations Zhao, T.; Dai, F.; Xu, N. W. Granular Matter, Vol. 17, Issue 6 https://doi.org/10.1007/s10035-015-0596-7	journal	September 2015
Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles Azema, Émilien; RadjaÏ, F.; Saussine, G. arXiv https://doi.org/10.48550/arxiv.0805.0178	text	January 2008
Maximum and Minimum Stable Random Packings of Platonic Solids Baker, Jessica; Kudrolli, Arshad arXiv https://doi.org/10.48550/arxiv.1008.1728	text	January 2010
Granular materials composed of shape-anisotropic grains Borzsonyi, Tamas; Stannarius, Ralf arXiv https://doi.org/10.48550/arxiv.1306.6214	text	January 2013
Granular flow down an inclined plane: Bagnold scaling and rheology Silbert, Leonardo E.; Ertaş, Deniz; Grest, Gary S. Physical Review E, Vol. 64, Issue 5 https://doi.org/10.1103/PhysRevE.64.051302	journal	October 2001
Optimal Filling of Shapes Phillips, Carolyn L.; Anderson, Joshua A.; Huber, Greg arXiv https://doi.org/10.48550/arxiv.1202.2450	text	January 2012
Critical scaling near jamming transition for frictional granular particles Otsuki, Michio; Hayakawa, Hisao Physical Review E, Vol. 83, Issue 5 https://doi.org/10.1103/PhysRevE.83.051301	journal	May 2011
Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure Azéma, Émilien; Radjaï, Farhang; Roux, Jean-Noël The European Physical Journal E, Vol. 41, Issue 1 https://doi.org/10.1140/epje/i2018-11608-9	journal	January 2018
Nonlinear effects of particle shape angularity in sheared granular media Azéma, Emilien; Estrada, Nicolas; Radjaï, Farhang Physical Review E, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevE.86.041301	journal	October 2012
Distinct element modelling of non-spherical frictionless particle flow Langston, Paul A.; Al-Awamleh, Mohammad A.; Fraige, Feras Y. Chemical Engineering Science, Vol. 59, Issue 2 https://doi.org/10.1016/j.ces.2003.10.008	journal	January 2004
Frictionless bead packs have macroscopic friction, but no dilatancy Peyneau, Pierre-Emmanuel; Roux, Jean-Noël arXiv https://doi.org/10.48550/arxiv.0802.1502	text	January 2008
Non-local rheology in dense granular flows: Revisiting the concept of fluidity Bouzid, Mehdi; Izzet, Adrien; Trulsson, Martin The European Physical Journal E, Vol. 38, Issue 11 https://doi.org/10.1140/epje/i2015-15125-1	journal	November 2015
Optimizing packing fraction in granular media composed of overlapping spheres Roth, Leah K.; Jaeger, Heinrich M. Soft Matter, Vol. 12, Issue 4 https://doi.org/10.1039/C5SM02335A	journal	January 2016
Flows of Dense Granular Media Forterre, Yoël; Pouliquen, Olivier Annual Review of Fluid Mechanics, Vol. 40, Issue 1 https://doi.org/10.1146/annurev.fluid.40.111406.102142	journal	January 2008
Rheology of three-dimensional packings of aggregates: Microstructure and effects of nonconvexity Azéma, Emilien; Radjaï, Farhang; Saint-Cyr, Baptiste Physical Review E, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevE.87.052205	journal	May 2013
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
Jamming of soft particles: geometry, mechanics, scaling and isostaticity van Hecke, M. Journal of Physics: Condensed Matter, Vol. 22, Issue 3 https://doi.org/10.1088/0953-8984/22/3/033101	journal	December 2009
Onset of mechanical stability in random packings of frictional spheres Jerkins, Melissa; Schröter, Matthias; Swinney, Harry L. arXiv https://doi.org/10.48550/arxiv.0710.5160	text	January 2007
Shear-driven segregation of dry granular materials with different friction coefficients Gillemot, Katalin A.; Somfai, Ellák; Börzsönyi, Tamás Soft Matter, Vol. 13, Issue 2 https://doi.org/10.1039/C6SM01946C	journal	January 2017
Granular shear flows at the elastic limit Campbell, Charles S. Journal of Fluid Mechanics, Vol. 465 https://doi.org/10.1017/S002211200200109X	journal	August 2002
Onset of Mechanical Stability in Random Packings of Frictional Spheres Jerkins, Melissa; Schröter, Matthias; Swinney, Harry L. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.018301	journal	July 2008
Geometry of Frictionless and Frictional Sphere Packings Silbert, Leonardo E.; Ertas, Deniz; Grest, Gary S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0111140	text	January 2001
Flow rule of dense granular flows down a rough incline Börzsönyi, Tamás; Ecke, Robert E. Physical Review E, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevE.76.031301	journal	September 2007
Jamming transition in emulsions and granular materials Zhang, H. P.; Makse, H. A. Physical Review E, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevE.72.011301	journal	July 2005
A discrete numerical model for granular assemblies Cundall, P. A.; Strack, O. D. L. Géotechnique, Vol. 29, Issue 1 https://doi.org/10.1680/geot.1979.29.1.47	journal	March 1979
Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids Donev, Aleksandar; Connelly, Robert; Stillinger, Frank H. Physical Review E, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevE.75.051304	journal	May 2007
Variable-cell method for stress-controlled jamming of athermal, frictionless grains Smith, Kyle C.; Srivastava, Ishan; Fisher, Timothy S. arXiv https://doi.org/10.48550/arxiv.1402.5563	text	January 2014
Effects of grain shape on packing and dilatancy of sheared granular materials Wegner, Sandra; Stannarius, Ralf; Boese, Axel Soft Matter, Vol. 10, Issue 28 https://doi.org/10.1039/c4sm00838c	journal	January 2014
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes Batten, Robert D.; Stillinger, Frank H.; Torquato, Salvatore Physical Review E, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevE.81.061105	journal	June 2010
Granular shear flows of flat disks and elongated rods without and with friction Guo, Y.; Wassgren, C.; Hancock, B. Physics of Fluids, Vol. 25, Issue 6 https://doi.org/10.1063/1.4812386	journal	June 2013
The coordination number of granular cylinders Blouwolff, J.; Fraden, S. Europhysics Letters (EPL), Vol. 76, Issue 6 https://doi.org/10.1209/epl/i2006-10376-1	journal	December 2006
Effects of grain shape on packing and dilatancy of sheared granular materials Wegner, Sandra; Stannarius, Ralf; Boese, Axel arXiv https://doi.org/10.48550/arxiv.1406.1301	text	January 2014
Particle shape consideration in numerical simulation of assemblies of irregularly shaped particles Abedi, Saba; Mirghasemi, Ali Asghar Particuology, Vol. 9, Issue 4 https://doi.org/10.1016/j.partic.2010.11.005	journal	August 2011
Random packing of nonspherical particles Nolan, G. T.; Kavanagh, P. E. Powder Technology, Vol. 84, Issue 3 https://doi.org/10.1016/0032-5910(95)98237-S	journal	September 1995
A clustered overlapping sphere algorithm to represent real particles in discrete element modelling Garcia, X.; Latham, J. -P.; Xiang, J. Géotechnique, Vol. 59, Issue 9 https://doi.org/10.1680/geot.8.T.037	journal	November 2009
Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity van Hecke, M. arXiv https://doi.org/10.48550/arxiv.0911.1384	text	January 2009
Optimal packings of superballs Jiao, Y.; Stillinger, F. H.; Torquato, S. Physical Review E, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevE.79.041309	journal	April 2009
A simulation study of the effects of dynamic variables on the packing of spheres Zhang, Z. P.; Liu, L. F.; Yuan, Y. D. Powder Technology, Vol. 116, Issue 1 https://doi.org/10.1016/S0032-5910(00)00356-9	journal	May 2001
Loose packings of frictional spheres Farrell, Greg R.; Martini, K. Michael; Menon, Narayanan Soft Matter, Vol. 6, Issue 13 https://doi.org/10.1039/c0sm00038h	journal	January 2010
Optimizing Packing Fraction in Granular Media Composed of Overlapping Spheres Roth, Leah K.; Jaeger, Heinrich M. arXiv https://doi.org/10.48550/arxiv.1510.05718	preprint	January 2015
Statistical characterization of microstructure of packings of polydisperse hard cubes Malmir, Hessam; Sahimi, Muhammad; Rahimi Tabar, M. Reza Physical Review E, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevE.95.052902	journal	May 2017
An experimental study of the elastic theory for granular flows Guo, Tongtong; Campbell, Charles S. Physics of Fluids, Vol. 28, Issue 8 https://doi.org/10.1063/1.4961096	journal	August 2016
Optimal Packings of Superballs Jiao, Yang; Stillinger, Frank; Torquato, Sal arXiv https://doi.org/10.48550/arxiv.0902.1504	text	January 2009
Rheophysics of dense granular materials: Discrete simulation of plane shear flows da Cruz, Frédéric; Emam, Sacha; Prochnow, Michaël Physical Review E, Vol. 72, Issue 2 https://doi.org/10.1103/PhysRevE.72.021309	journal	August 2005
Phase diagram for inertial granular flows DeGiuli, E.; McElwaine, J. N.; Wyart, M. Physical Review E, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevE.94.012904	journal	July 2016
A numerical study on the influence of particle shape on hopper discharge within the polyhedral and multi-sphere discrete element method Höhner, D.; Wirtz, S.; Scherer, V. Powder Technology, Vol. 226 https://doi.org/10.1016/j.powtec.2012.03.041	journal	August 2012
DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge Cleary, Paul W.; Sawley, Mark L. Applied Mathematical Modelling, Vol. 26, Issue 2 https://doi.org/10.1016/S0307-904X(01)00050-6	journal	February 2002
Experiments on the Random Packing of Tetrahedral Dice Jaoshvili, Alexander; Esakia, Andria; Porrati, Massimo Physical Review Letters, Vol. 104, Issue 18 https://doi.org/10.1103/PhysRevLett.104.185501	journal	May 2010
Experiments on Random Packings of Ellipsoids Man, Weining; Donev, Aleksandar; Stillinger, Frank H. Physical Review Letters, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevLett.94.198001	journal	May 2005
Jamming of three-dimensional prolate granular materials Desmond, K.; Franklin, Scott V. Physical Review E, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevE.73.031306	journal	March 2006
Effect of particle surface friction on nonlocal constitutive behavior of flowing granular media Kamrin, Ken; Koval, Georg Computational Particle Mechanics, Vol. 1, Issue 2 https://doi.org/10.1007/s40571-014-0018-3	journal	May 2014
Rheology of granular materials composed of nonconvex particles Saint-Cyr, B.; Delenne, J. -Y.; Voivret, C. Physical Review E, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevE.84.041302	journal	October 2011
A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles Schreck, Carl F.; Xu, Ning; O'Hern, Corey S. Soft Matter, Vol. 6, Issue 13 https://doi.org/10.1039/c001085e	journal	January 2010
Friction in inertial granular flows: competition between dilation and grain-scale dissipation rates Hurley, Ryan C.; Andrade, José E. Granular Matter, Vol. 17, Issue 3 https://doi.org/10.1007/s10035-015-0564-2	journal	May 2015
Optimal Filling of Shapes Phillips, Carolyn L.; Anderson, Joshua A.; Huber, Greg Physical Review Letters, Vol. 108, Issue 19 https://doi.org/10.1103/PhysRevLett.108.198304	journal	May 2012
A novel method based on orientation discretization for discrete element modeling of non-spherical particles Dong, Kejun; Wang, Chuncheng; Yu, Aibing Chemical Engineering Science, Vol. 126 https://doi.org/10.1016/j.ces.2014.12.059	journal	April 2015
Dynamics of gas–solid fluidised beds with non-spherical particle geometry Hilton, J. E.; Mason, L. R.; Cleary, P. W. Chemical Engineering Science, Vol. 65, Issue 5 https://doi.org/10.1016/j.ces.2009.10.028	journal	March 2010
Force transmission in a packing of pentagonal particles Azéma, Emilien; Radjaï, Farhang; Peyroux, Robert Physical Review E, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRevE.76.011301	journal	July 2007
Dry granular flows: Rheological measurements of the μ(I)-rheology Fall, A.; Ovarlez, G.; Hautemayou, D. Journal of Rheology, Vol. 59, Issue 4 https://doi.org/10.1122/1.4922653	journal	July 2015
Quasistatic rheology and microstructural description of sheared granular materials composed of platy particles Boton, Mauricio; Azéma, Emilien; Estrada, Nicolas Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.032206	journal	March 2013
Isostaticity of constraints in amorphous jammed systems of soft frictionless Platonic solids Smith, Kyle C.; Fisher, Timothy S.; Alam, Meheboob Physical Review E, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevE.84.030301	journal	September 2011
Distinctive features arising in maximally random jammed packings of superballs Jiao, Y.; Stillinger, F. H.; Torquato, S. Physical Review E, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevE.81.041304	journal	April 2010
Jamming of frictional spheres and random loose packing Silbert, Leonardo E. Soft Matter, Vol. 6, Issue 13 https://doi.org/10.1039/c001973a	journal	January 2010
Rheology and dynamics of colloidal superballs Royer, John R.; Burton, George L.; Blair, Daniel L. Soft Matter, Vol. 11, Issue 28 https://doi.org/10.1039/C5SM00729A	journal	January 2015
Frictionless bead packs have macroscopic friction, but no dilatancy Peyneau, Pierre-Emmanuel; Roux, Jean-Noël Physical Review E, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevE.78.011307	journal	July 2008
An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers Džiugys, Algis; Peters, Bernhard Granular Matter, Vol. 3, Issue 4 https://doi.org/10.1007/PL00010918	journal	December 2001
Geometry of frictionless and frictional sphere packings Silbert, Leonardo E.; Ertaş, Deniz; Grest, Gary S. Physical Review E, Vol. 65, Issue 3 https://doi.org/10.1103/PhysRevE.65.031304	journal	February 2002

Cited By (4)

Jammed packings of 3D superellipsoids with tunable packing fraction, coordination number, and ordering Yuan, Ye; VanderWerf, Kyle; Shattuck, Mark D. Soft Matter, Vol. 15, Issue 47 https://doi.org/10.1039/c9sm01932d	journal	January 2019
Flow-Arrest Transitions in Frictional Granular Matter Srivastava, Ishan; Silbert, Leonardo E.; Grest, Gary S. Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/physrevlett.122.048003	journal	January 2019
Energy Partitioning in Granular Flow Depends on Mineralogy via Nanoscale Plastic Work Taylor, S. E.; Brodsky, E. E. Journal of Geophysical Research: Solid Earth, Vol. 124, Issue 7 https://doi.org/10.1029/2019jb017762	journal	July 2019
Flow-Arrest Transitions in Frictional Granular Matter Srivastava, Ishan; Silbert, Leonardo E.; Grest, Gary S. arXiv https://doi.org/10.48550/arxiv.1810.00043	text	January 2018

Similar Records

Fluctuations and power-law scaling of dry, frictionless granular rheology near the hard-particle limit

Journal Article · 2022 · Physical Review Fluids (Online) · OSTI ID:1906681

Santos, Andrew P.; Srivastava, Ishan; Silbert, Leonardo E.; +2 more

LLNL granular solids flow project: Quarterly report, July-September 1987

Technical Report · 1987 · OSTI ID:5274488

Walton, O R

Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows

Journal Article · 2015 · Physics of Fluids (1994) · OSTI ID:22403207

Berzi, Diego; Vescovi, Dalila

Related Subjects

36 MATERIALS SCIENCE

Title: Effect of shape and friction on the packing and flow of granular materials

Citation Formats

References (85)

Cited By (4)

Similar Records

Related Subjects