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arxiv: 2604.20102 · v1 · submitted 2026-04-22 · ❄️ cond-mat.soft · cond-mat.stat-mech

Unjamming in a 3D Granular System: The Micromechanical Role of Friction in Force Distributions and Rheological Properties

Vicente Salinas , H\'ector Alarc\'on , Eduardo Rojas , Pablo Guti\'errez , Gustavo Castillo This is my paper

Pith reviewed 2026-05-09 23:57 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords granular unjammingfrictional spheresforce distributionscoordination numberdiscrete element methodpacking fraction3D granular systemsrheological properties
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The pith

Friction shapes force distributions and coordination during unjamming of 3D frictional spheres by random particle removal.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the unjamming transition in a three-dimensional assembly of frictional spheres where packing fraction decreases through successive random particle extractions. Discrete element simulations track how interparticle forces, coordination numbers, and density evolve as a function of the friction coefficient. Results indicate that friction produces distinct relationships in both structural and mechanical quantities that remain consistent with patterns documented in other granular systems. This matters because it suggests friction's influence on force networks and contact loss is not tied to the specific way density is reduced. A reader would see value in recognizing that the same friction dependencies appear across driving mechanisms, pointing toward more general descriptions of granular stability and flow.

Core claim

In simulations of frictional spheres, systematic random particle extractions reduce the packing fraction and produce friction-dependent evolutions in interparticle force distributions, coordination numbers, and overall rheological response; these evolutions match qualitative trends previously reported for dense granular materials even though the driving mechanism differs from shear or vibration.

What carries the argument

The interparticle friction coefficient, which controls the statistics of contact forces and the rate of contact loss as particles are randomly removed.

If this is right

  • Higher friction coefficients produce broader force distributions that persist as density decreases.
  • The average coordination number declines at different rates depending on the friction coefficient.
  • Rheological measures such as stress and strain-rate relations retain friction-sensitive trends through the transition.
  • Qualitative agreement with prior dense-granular observations holds despite the change in unjamming protocol.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same friction dependence might govern unjamming in natural settings where particles are lost by dissolution or erosion rather than mechanical agitation.
  • Design rules for granular silos or hoppers could incorporate friction-tuned coordination thresholds to predict flow initiation.
  • Direct 3D imaging of contact forces in model granular packs could test whether the simulated force statistics survive in laboratory random-removal setups.

Load-bearing premise

Random particle extraction generates an unjamming process whose local force and contact properties are comparable to those produced by shear or vibration.

What would settle it

Force probability distributions or coordination-number curves measured in a random-extraction experiment that show no friction dependence, while the same curves in a shear experiment do, would falsify the claimed consistency.

Figures

Figures reproduced from arXiv: 2604.20102 by Eduardo Rojas, Gustavo Castillo, H\'ector Alarc\'on, Pablo Guti\'errez, Vicente Salinas.

Figure 1
Figure 1. Figure 1: No external shear or directional forcing is applied. The evolution of the system is driven [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: a) A snapshot of the numerical setup used in the simulations. A box with solid lateral walls whose size is Lx = Ly = 24d is initially filled with N = 30000 spheres of diameter d = 1 mm. Every ∆te = 0.02 s, Ne = 30 random particles are removed from the bottom half of the box (blue particles in the figure). Thus, in our setup, the packing fraction is influenced by the particle-removal protocol. As particles … view at source ↗
Figure 2
Figure 2. Figure 2: a) Number of particles with kinetic energy exceeding the threshold Kc = (1/5) mgd for µp = 0.8. Two distinct regimes are observed during particle extraction: an initial regime in which this number increases in time, followed by a second regime where it reaches a saturation value. The red curve corresponds to the smoothed data. Insets show snapshots of the system in each regime; particles satisfying the kin… view at source ↗
Figure 3
Figure 3. Figure 3: a) Mean coordination number versus time for different friction coefficients. The data show a monotonic, nearly linear decrease in the number of contacts as particles are removed, eventually reaching an asymptotic plateau Zc. This critical value represents the mechanical limit of the system just prior to the unjamming transition. b) Critical coordination number as a function of interparticle friction. c) Pa… view at source ↗
Figure 4
Figure 4. Figure 4: a) Probability Density Function (PDF) of the normal forces at three different times for µp = 0.4. All distributions are normalized to unit area (R P(ζ)dζ = 1). This distribution exhibits a power law for low forces and an exponential decay for high forces. The inset shows an example of the fit PDF = A exp(−(fn/f¯n) c ). The dashed vertical line indicates the mean force for that particular data set. b) Time … view at source ↗
Figure 5
Figure 5. Figure 5: a) Probability density function of the plasticity index ζ ≡ ft/µpfn. The PDF are displayed at t = 300. b) Average plasticity index ⟨ζ⟩ ≡ ⟨ft/µpfn⟩ versus time. Each color corresponds to a different friction coefficient µp in the range 0.2 (blue) to 0.9 (dark red). c) Plasticity index once the system reached the critical point. The fit corresponds to a rational function ζc = p0 µp+q0 , with p0 = 0.4747, q0 … view at source ↗
Figure 6
Figure 6. Figure 6: a) Gini factor of the plasticity index, Gζ as a function of time for different friction coefficients µp. Each color corresponds to a different friction coefficient µp in the range 0.2 (blue) to 0.9 (dark red). b) Gini factor after the system reached the final jammed state (t ≳ 100). 0 50 100 150 200 250 300 350 2 2.5 3 3.5 ·104 a) µp t F 0 50 100 150 200 250 300 350 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 b)… view at source ↗
Figure 7
Figure 7. Figure 7: a) Chain forces intensity as a function of time for all the interparticle friction coefficients explored. b) Gini coefficient of the chain force intensity as a function of time. Inset shows the critical value of the Gini coefficient of the chain forces. The dashed line corresponds to the mean value of this coefficient (⟨GF c ⟩ = 0.284) over all µp. Each color corresponds to a different friction coefficient… view at source ↗
read the original abstract

In this work, we investigate the unjamming transition in a three-dimensional granular system composed of frictional spheres, in which the packing fraction is systematically reduced by random particle extractions. Using Discrete Element Method (DEM) simulations, we analyze the evolution of key micro-mechanical quantities, such as the interparticle forces, the coordination number and the overall packing density as a function of the interparticle friction coefficient. Our results reveal friction-dependent relationships on structural as well as mechanical observables, and exhibit trends that are qualitatively consistent with observations reported in dense granular systems. These trends persist despite the very different driving mechanism considered here. This paper is part of the thematic issue \emph{``Sand, silos and asteroids: clustering challenges in granular materials research''}.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates the unjamming transition in a 3D system of frictional spheres by systematically lowering the packing fraction through random particle extractions in DEM simulations. It examines the evolution of interparticle forces, coordination number, and packing density as functions of the friction coefficient, reporting friction-dependent trends in structural and mechanical observables that are claimed to be qualitatively consistent with those observed in dense granular systems under other driving mechanisms.

Significance. If the protocol produces representative unjamming states, the work would add to the understanding of friction's micromechanical role in 3D granular unjamming by providing detailed force and coordination data. The DEM approach enables access to microscale quantities, and the persistence of trends despite a non-standard driving mechanism is potentially useful for the thematic issue on granular clustering challenges. However, without explicit validation against shear- or vibration-driven benchmarks, the broader significance remains conditional.

major comments (1)
  1. [§2] §2 (Methods): The unjamming protocol of instantaneous random particle removal followed by relaxation is not shown to produce contact networks or force statistics equivalent to quasi-static shear or vibration protocols used in the cited literature. The central claim of qualitative consistency with dense granular systems therefore requires either a direct overlay of force PDFs, Z(φ) curves, or other observables against literature data or a quantitative justification that the random-extraction states are in the same universality class; neither appears to be provided.
minor comments (2)
  1. Figures showing force distributions and coordination number vs. packing fraction should include error bars or ensemble statistics to allow assessment of trend robustness.
  2. Clarify the precise definition of the coordination number (e.g., whether rattlers are excluded) and the friction coefficient range explored, as these details affect comparability with prior work.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for identifying the need to clarify the scope of our claims regarding the unjamming protocol. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [§2] §2 (Methods): The unjamming protocol of instantaneous random particle removal followed by relaxation is not shown to produce contact networks or force statistics equivalent to quasi-static shear or vibration protocols used in the cited literature. The central claim of qualitative consistency with dense granular systems therefore requires either a direct overlay of force PDFs, Z(φ) curves, or other observables against literature data or a quantitative justification that the random-extraction states are in the same universality class; neither appears to be provided.

    Authors: We agree that the random particle removal protocol differs from quasi-static shear or vibration protocols. However, the manuscript's central claim is not that the resulting contact networks or force statistics are equivalent, nor that the states belong to the same universality class. Rather, we report that friction-dependent trends in force distributions, coordination number, and density persist under this distinct driving mechanism. This robustness to protocol is itself a key observation supporting the micromechanical role of friction. We do not provide direct overlays of PDFs or Z(φ) curves because our study does not aim for quantitative equivalence with specific literature datasets; reproducing identical conditions from prior works would require new, extensive simulations outside the present scope. In the revised manuscript we will add explicit discussion in the Methods and Conclusions sections clarifying the protocol differences, the qualitative nature of the consistency claim, and the physical rationale for expecting similar friction trends across mechanisms. This addresses the referee's concern by strengthening the justification without new data. revision: partial

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs with no derivations or self-referential fits

full rationale

The paper uses DEM simulations to extract particles randomly and relax the system, then reports observed trends in force distributions, coordination number, and packing density versus friction coefficient. No equations, fitted parameters, or predictions are defined in terms of themselves. Claims of qualitative consistency with prior literature are external comparisons, not load-bearing self-citations or uniqueness theorems. The central results reduce only to the simulation protocol and measured quantities, with no reduction by construction to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not introduce or specify any free parameters, axioms, or invented entities; the work relies on standard Discrete Element Method simulations of frictional spheres without additional postulates.

pith-pipeline@v0.9.0 · 5448 in / 1103 out tokens · 35761 ms · 2026-05-09T23:57:13.204180+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

46 extracted references · 40 canonical work pages

  1. [1]

    Physical Review E—Statistical, Nonlinear, and Soft Matter Physics , volume=

    Bridging the rheology of granular flows in three regimes , author=. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics , volume=. 2012 , publisher=

    2012

  2. [2]

    Physics of fluids , volume=

    Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows , author=. Physics of fluids , volume=. 2015 , publisher=

    2015

  3. [3]

    Journal of Fluid Mechanics , volume=

    A constitutive model with microstructure evolution for flow of rate-independent granular materials , author=. Journal of Fluid Mechanics , volume=. 2011 , publisher=

    2011

  4. [4]

    2025 , title =

    Lambert, Clovis and Maurin, Raphaël and Lacaze, Laurent and Fede, Pascal , journal =. 2025 , title =. doi:10.1103/physrevfluids.10.034301 , pages =

    work page doi:10.1103/physrevfluids.10.034301 2025

  5. [5]

    1954 , title =

    Bagnold, Ralph Alger , journal =. 1954 , title =. doi:10.1098/rspa.1954.0186 , pages =

    work page doi:10.1098/rspa.1954.0186 1954

  6. [6]

    2014 , title =

    Behringer, R P and Bi, D and Chakraborty, B and Clark, A and Dijksman, J and Ren, J and Zhang, J , journal =. 2014 , title =. doi:10.1088/1742-5468/2014/06/p06004 , pages =

    work page doi:10.1088/1742-5468/2014/06/p06004 2014

  7. [7]

    Nature Physics , issn =

    Jamming: A new kind of phase transition? , author =. Nature Physics , issn =. 2007 , rating =. doi:10.1038/nphys580 , url =

    work page doi:10.1038/nphys580 2007

  8. [8]

    Fluctuations and criticality of a granular solid-liquid-Like phase transition.Phys

    Fluctuations and Criticality of a Granular Solid-Liquid-Like Phase Transition , author =. Physical Review Letters , issn =. 2012 , rating =. doi:10.1103/physrevlett.109.095701 , pmid =. 1204.0059 , pages =

    work page doi:10.1103/physrevlett.109.095701 2012

  9. [9]

    Physical Review E , issn =

    Rheophysics of dense granular materials: Discrete simulation of plane shear flows , author =. Physical Review E , issn =. 2005 , rating =. doi:10.1103/physreve.72.021309 , pmid =. cond-mat/0503682 , pages =

    work page doi:10.1103/physreve.72.021309 2005

  10. [10]

    G´ eotechnique29(1), 47–65 (1979) https:// doi.org/10.1680/geot.1979.29.1.47

    Cundall, P A and Strack, O D L , journal =. 1979 , title =. doi:10.1680/geot.1979.29.1.47 , pages =

    work page doi:10.1680/geot.1979.29.1.47 1979

  11. [11]

    1999 , title =

    Daerr, Adrian and Douady, Stéphane , journal =. 1999 , title =. doi:10.1038/20392 , pages =

    work page doi:10.1038/20392 1999

  12. [12]

    and Hayman, Nicholas W

    Daniels, Karen E. and Hayman, Nicholas W. , journal =. 2008 , title =. doi:10.1029/2008jb005781 , number =

    work page doi:10.1029/2008jb005781 2008

  13. [13]

    1987 , title =

    Dixon, Philip M and Weiner, Jacob and Mitchell-Olds, Thomas and Woodley, Robert , journal =. 1987 , title =

    1987

  14. [14]

    and Abramian, A

    Gans, A. and Abramian, A. and Lagrée, P.-Y. and Gong, M. and Sauret, A. and Pouliquen, O. and Nicolas, M. , journal =. 2023 , title =. doi:10.1017/jfm.2023.180 , pages =

    work page doi:10.1017/jfm.2023.180 2023

  15. [15]

    Variabilità e mutabilità: contributo allo studio delle distribuzioni e delle relazioni statistiche , author =

  16. [16]

    2015 , title =

    Guo, Yu and Curtis, Jennifer Sinclair , journal =. 2015 , title =. doi:10.1146/annurev-fluid-010814-014644 , pages =

    work page doi:10.1146/annurev-fluid-010814-014644 2015

  17. [17]

    2016 , title =

    Gutiérrez, Francisco , doi =. 2016 , title =

    2016

  18. [18]

    Physical Review Letters , issn =

    Quantifying Interparticle Forces and Heterogeneity in 3D Granular Materials , author =. Physical Review Letters , issn =. 2016 , rating =. doi:10.1103/physrevlett.117.098005 , pmid =

    work page doi:10.1103/physrevlett.117.098005 2016

  19. [19]

    Granular solids, liquids, and gases.Rev

    Granular solids, liquids, and gases , author =. Reviews of Modern Physics , issn =. 1996 , rating =. doi:10.1103/revmodphys.68.1259 , pages =

    work page doi:10.1103/revmodphys.68.1259 1996

  20. [20]

    2006 , title =

    Jop, Pierre and Forterre, Yoël and Pouliquen, Olivier , journal =. 2006 , title =. doi:10.1038/nature04801 , pmid =. cond-mat/0612110 , pages =

    work page doi:10.1038/nature04801 2006

  21. [21]

    Nature , issn =

    Jamming is not just cool any more , author =. Nature , issn =. 1998 , rating =. doi:10.1038/23819 , pages =

    work page doi:10.1038/23819 1998

  22. [22]

    and Nagel, S

    Liu, C.-H. and Nagel, S. R. and Schecter, D. A. and Coppersmith, S. N. and Majumdar, S. and Narayan, O. and Witten, T. A. , journal =. 1995 , title =. doi:10.1126/science.269.5223.513 , pmid =

    work page doi:10.1126/science.269.5223.513 1995

  23. [23]

    2008 , title =

    Luding, Stefan , journal =. 2008 , title =. doi:10.1007/s10035-008-0099-x , pages =

    work page doi:10.1007/s10035-008-0099-x 2008

  24. [24]

    and Hill, Kimberly M

    Man, Teng and Zhang, Pei and Ge, Zhuan and Galindo-Torres, Sergio A. and Hill, Kimberly M. , journal =. 2023 , title =. doi:10.1007/s10409-022-22191-x , pages =

    work page doi:10.1007/s10409-022-22191-x 2023

  25. [25]

    Physical Review E , issn =

    Jamming at zero temperature and zero applied stress: The epitome of disorder , author =. Physical Review E , issn =. 2003 , rating =. doi:10.1103/physreve.68.011306 , pmid =. cond-mat/0304421 , url =

    work page doi:10.1103/physreve.68.011306 2003

  26. [26]

    Physical Review Letters , issn =

    Random Packings of Frictionless Particles , author =. Physical Review Letters , issn =. 2002 , rating =. doi:10.1103/physrevlett.88.075507 , pmid =. cond-mat/0110644 , url =

    work page doi:10.1103/physrevlett.88.075507 2002

  27. [27]

    and Liniger, Eric G

    Onoda, George Y. and Liniger, Eric G. , journal =. 1990 , title =. doi:10.1103/physrevlett.64.2727 , pmid =

    work page doi:10.1103/physrevlett.64.2727 1990

  28. [28]

    and Shattuck, Mark D

    Papanikolaou, Stefanos and O’Hern, Corey S. and Shattuck, Mark D. , journal =. 2013 , title =. doi:10.1103/physrevlett.110.198002 , pmid =. 1207.6010 , pages =

    work page doi:10.1103/physrevlett.110.198002 2013

  29. [29]

    Physical Review E , issn =

    Characterization of force chains in granular material , author =. Physical Review E , issn =. 2005 , rating =. doi:10.1103/physreve.72.041307 , pmid =

    work page doi:10.1103/physreve.72.041307 2005

  30. [30]

    and Bideau, D

    Philippe, P. and Bideau, D. , journal =. 2002 , title =. doi:10.1209/epl/i2002-00362-7 , eprint =

    work page doi:10.1209/epl/i2002-00362-7 2002

  31. [31]

    2006 , title =

    Pouliquen, O and Cassar, C and Jop, P and Forterre, Y and Nicolas, M , journal =. 2006 , title =. doi:10.1088/1742-5468/2006/07/p07020 , pages =

    work page doi:10.1088/1742-5468/2006/07/p07020 2006

  32. [32]

    Physical Review Letters , issn =

    Bimodal Character of Stress Transmission in Granular Packings , author =. Physical Review Letters , issn =. 1998 , rating =. doi:10.1103/physrevlett.80.61 , pages =

    work page doi:10.1103/physrevlett.80.61 1998

  33. [33]

    Raynaud, J. S. and Moucheront, P. and Baudez, J. C. and Bertrand, F. and Guilbaud, J. P. and Coussot, P. , journal =. 2002 , title =. doi:10.1122/1.1463420 , pages =

    work page doi:10.1122/1.1463420 2002

  34. [34]

    Physical Review E , issn =

    Stability of a tilted granular monolayer: How many spheres can we pick before the collapse? , author =. Physical Review E , issn =. 2023 , rating =. doi:10.1103/physreve.108.064904 , pages =

    work page doi:10.1103/physreve.108.064904 2023

  35. [35]

    2000 , title =

    Roux, Jean-Noël , journal =. 2000 , title =. doi:10.1103/physreve.61.6802 , pmid =. cond-mat/0001246 , pages =

    work page doi:10.1103/physreve.61.6802 2000

  36. [36]

    1996 , title =

    Shäfer, J and Dippel, S and Wolf, D E , journal =. 1996 , title =. doi:10.1051/jp1:1996129 , pages =

    work page doi:10.1051/jp1:1996129 1996

  37. [37]

    , journal =

    Silbert, Leonardo E. , journal =. 2010 , title =. doi:10.1039/c001973a , eprint =

    work page doi:10.1039/c001973a 2010

  38. [38]

    and Ertaş, Deniz and Grest, Gary S

    Silbert, Leonardo E. and Ertaş, Deniz and Grest, Gary S. and Halsey, Thomas C. and Levine, Dov , journal =. 2002 , title =. doi:10.1103/physreve.65.031304 , pmid =

    work page doi:10.1103/physreve.65.031304 2002

  39. [39]

    Nature 453, 629–632 (2008)

    A phase diagram for jammed matter , author =. Nature , issn =. 2008 , rating =. doi:10.1038/nature06981 , pmid =

    work page doi:10.1038/nature06981 2008

  40. [40]

    and Lechman, Jeremy B

    Srivastava, Ishan and Silbert, Leonardo E. and Lechman, Jeremy B. and Grest, Gary S. , journal =. 2022 , title =. doi:10.1039/d1sm01344k , pages =

    work page doi:10.1039/d1sm01344k 2022

  41. [41]

    International Journal of Modern Physics C , issn =

    Modeling of particle size segregation: Calibration using the discrete particle method , author =. International Journal of Modern Physics C , issn =. 2012 , rating =. doi:10.1142/s0129183112400141 , pages =

    work page doi:10.1142/s0129183112400141 2012

  42. [42]

    Physical Review Letters , issn =

    Stresses in Silos: Comparison Between Theoretical Models and New Experiments , author =. Physical Review Letters , issn =. 2000 , rating =. doi:10.1103/physrevlett.84.1439 , pmid =. cond-mat/9904094 , pages =

    work page doi:10.1103/physrevlett.84.1439 2000

  43. [43]

    Weinhart, L

    Weinhart, Thomas and Orefice, Luca and Post, Mitchel and Lantman, Marnix P. van Schrojenstein and Denissen, Irana F.C. and Tunuguntla, Deepak R. and Tsang, J.M.F. and Cheng, Hongyang and Shaheen, Mohamad Yousef and Shi, Hao and Rapino, Paolo and Grannonio, Elena and Losacco, Nunzio and Barbosa, Joao and Jing, Lu and Naranjo, Juan E. Alvarez and Roy, Sudes...

    work page doi:10.1016/j.cpc.2019.107129 2020

  44. [44]

    Granular Matter , issn =

    Closure relations for shallow granular flows from particle simulations , author =. Granular Matter , issn =. 2012 , rating =. doi:10.1007/s10035-012-0355-y , pages =

    work page doi:10.1007/s10035-012-0355-y 2012

  45. [45]

    2012 , title =

    Yitzhaki, Shlomo and Schechtman, Edna , journal =. 2012 , title =. doi:10.1007/978-1-4614-4720-7 , pages =

    work page doi:10.1007/978-1-4614-4720-7 2012

  46. [46]

    2014 , title =

    Zhang, Ling and Wang, Yujie and Zhang, Jie , journal =. 2014 , title =. doi:10.1103/physreve.89.012203 , pmid =

    work page doi:10.1103/physreve.89.012203 2014