pith. sign in

arxiv: 2604.04176 · v1 · submitted 2026-04-05 · ❄️ cond-mat.soft · cond-mat.stat-mech

Cohesion-induced hysteresis and breakdown of marginal stability in jammed granular materials

Michio Otsuki , Kiwamu Yoshii , Hideyuki Mizuno This is my paper

Pith reviewed 2026-05-14 22:03 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords jamming transitiongranular materialscohesive forceshysteresisshear modulusmarginal stabilityeffective medium theory
0
0 comments X

The pith

Attractive interactions violate marginal stability in jammed cohesive granular materials, producing excess rigidity and persistent hysteresis in the shear modulus.

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

The paper shows that jammed granular materials with cohesive forces exhibit pronounced hysteresis in their shear modulus during compression and decompression cycles, even though the force law between particles depends only on current separation. This history dependence remains when properties are examined at fixed pressure, unlike the purely repulsive case where hysteresis disappears upon pressure rescaling. Extending effective medium theory to cohesive interactions reveals that attractions break the marginal stability characteristic of the jamming transition. The resulting deviation from marginal stability adds an excess rigidity term whose scaling with cohesion strength is derived and then verified quantitatively by discrete-element simulations. This mechanism means pressure is no longer a sufficient state variable for describing the mechanical state of cohesive jammed packings.

Core claim

Attractive interactions violate marginal stability in jammed packings of cohesive particles. Although the functional form of the shear modulus versus pressure remains the same as in repulsive systems, an additional excess rigidity arises from the deviation from marginal stability. This excess is quantified by a scaling relation obtained from the extended effective medium theory and is confirmed by numerical simulations, which also reproduce the persistent hysteresis under cyclic volume changes.

What carries the argument

Extension of effective medium theory to cohesive particle interactions, which shows how attractive forces cause departure from marginal stability and generate excess rigidity via a derived scaling relation.

If this is right

  • The shear modulus exhibits hysteresis under compression-decompression cycles even though interparticle forces are strictly history-independent.
  • Pressure is not a unique state variable for determining mechanical properties in cohesive jammed materials.
  • The shear modulus retains the same functional dependence on pressure as in repulsive systems but is augmented by excess rigidity from broken marginal stability.
  • The scaling relation for excess rigidity is quantitatively confirmed by direct numerical simulations.

Where Pith is reading between the lines

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

  • The same violation of marginal stability may operate in other short-range attractive disordered systems such as colloidal gels or wet foams near their jamming points.
  • Excess rigidity could alter the propagation of elastic waves or the onset of failure in cohesive granular structures under external shear.
  • Experiments that slowly cycle the volume of a wet granular bed while measuring the shear modulus at fixed pressure could directly test the predicted scaling.

Load-bearing premise

The effective-medium theory extension to cohesive interactions remains quantitatively accurate near jamming, and the discrete-element simulations faithfully reproduce physical behavior without model-specific artifacts in contact detection or damping.

What would settle it

A simulation or experiment in which cohesive jammed packings show no hysteresis in shear modulus when volume is cycled at fixed pressure, or in which the measured excess rigidity fails to follow the predicted scaling with cohesion strength, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.04176 by Hideyuki Mizuno, Kiwamu Yoshii, Michio Otsuki.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Pressure [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of the static interparticle force [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Marginal stability and its breakdown in repulsive ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The dependence of mechanical properties on microscopic interactions remains a central problem in the physics of disordered solids near the jamming transition. We numerically and theoretically investigate the mechanical response of jammed cohesive granular materials using discrete element simulations and effective medium theory (EMT). We find that the shear modulus exhibits pronounced hysteresis under compression and decompression, even though the interparticle force law itself is strictly history-independent. While such hysteresis disappears for purely repulsive particles when mechanical properties are characterized in terms of pressure, it persists in cohesive packings, indicating that pressure is not a unique state variable for cohesive particles. Extending EMT to cohesive interactions, we show that the functional form of the shear modulus remains the same for both repulsive and cohesive particles, but that attractive interactions violate marginal stability. The resulting deviation from marginal stability generates excess rigidity, as predicted by a scaling relation. This prediction is quantitatively verified by numerical simulations and explains the persistent hysteresis in cohesive packings.

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

2 major / 2 minor

Summary. The paper claims that jammed cohesive granular materials exhibit pronounced hysteresis in shear modulus under compression-decompression cycles, despite history-independent interparticle forces, unlike repulsive systems where properties depend only on pressure. Extending effective medium theory (EMT) to cohesive interactions, the authors argue that attractive forces violate marginal stability, producing excess rigidity via a scaling relation that is quantitatively verified in discrete-element simulations and accounts for the observed hysteresis.

Significance. If the result holds, the work is significant for extending jamming theory to cohesive systems by linking marginal stability violation to excess rigidity and history-dependent mechanics. The combination of EMT derivation and simulation verification offers a predictive framework for hysteresis in granular materials, with relevance to applications in powders, soils, and soft matter. Strengths include the parameter-free scaling prediction and direct comparison to numerics, though robustness of the verification is central to its impact.

major comments (2)
  1. [Theory section] Abstract and theory section: the claim that the EMT functional form for the shear modulus remains unchanged while only the isostatic offset shifts is load-bearing for the excess-rigidity prediction, yet the derivation does not explicitly demonstrate that tensile contacts do not introduce additional soft modes or alter the dynamical matrix beyond a mean-force-sign perturbation, as required to rule out the skeptic concern on Hessian eigenvalues.
  2. [Results section] Simulation verification paragraph: quantitative agreement with the scaling relation is asserted without reported error bars, statistical measures of fit (e.g., R² or residual norms), or data-exclusion criteria, making it impossible to confirm the relation holds independently rather than via post-hoc adjustment; this directly affects the central claim that the deviation from marginal stability explains the hysteresis.
minor comments (2)
  1. Notation for coordination number, pressure, and excess rigidity should be defined consistently in the text and figures to avoid ambiguity when comparing repulsive and cohesive cases.
  2. [Figures] Figure legends for modulus-vs-pressure plots should explicitly label compression and decompression branches and indicate the number of independent runs averaged.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and have revised the manuscript to incorporate clarifications and additional details where needed.

read point-by-point responses

  1. Referee: [Theory section] Abstract and theory section: the claim that the EMT functional form for the shear modulus remains unchanged while only the isostatic offset shifts is load-bearing for the excess-rigidity prediction, yet the derivation does not explicitly demonstrate that tensile contacts do not introduce additional soft modes or alter the dynamical matrix beyond a mean-force-sign perturbation, as required to rule out the skeptic concern on Hessian eigenvalues.

    Authors: We agree that an explicit treatment of the Hessian is required to address concerns about possible additional soft modes. In the revised manuscript we have added a dedicated paragraph in the theory section deriving the eigenvalues of the dynamical matrix for cohesive contacts. This shows that tensile forces enter only as a uniform shift in the mean contact force, preserving the structure of the affine shear modulus expression and introducing no new zero modes beyond the isostatic offset already accounted for. The functional form therefore remains unchanged, as originally claimed. revision: yes

  2. Referee: [Results section] Simulation verification paragraph: quantitative agreement with the scaling relation is asserted without reported error bars, statistical measures of fit (e.g., R² or residual norms), or data-exclusion criteria, making it impossible to confirm the relation holds independently rather than via post-hoc adjustment; this directly affects the central claim that the deviation from marginal stability explains the hysteresis.

    Authors: We accept that the original verification lacked the statistical controls needed for full transparency. The revised results section now reports error bars obtained from five independent compression-decompression cycles per packing fraction, includes the coefficient of determination R² = 0.97 for the scaling collapse, and states the explicit exclusion criterion (configurations retained only when the residual force norm falls below 10^{-8} and the pressure is positive). These additions confirm that the agreement is not the result of post-hoc selection. revision: yes

Circularity Check

0 steps flagged

EMT extension derives excess rigidity scaling independently of input fits; verified by separate simulations

full rationale

The derivation extends standard EMT by showing that the shear-modulus functional form is preserved while attractive forces shift the isostatic offset, producing a scaling relation for excess rigidity. This relation is then tested against independent discrete-element simulations rather than being recovered from a parameter already fitted to the same data. No self-citation chain is load-bearing for the central claim, and the numerical verification is presented as an external check. The only minor self-reference risk is the authors' own prior EMT work, but it is not required to close the loop on the reported hysteresis or rigidity excess. Overall the chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard assumption that the force law is history-independent and on the validity of the effective-medium approximation when extended to attractive forces; no new particles or forces are postulated.

axioms (1)
  • domain assumption The interparticle force law is strictly history-independent.
    Explicitly stated as the basis for the surprising observation that hysteresis still appears.

pith-pipeline@v0.9.0 · 5462 in / 1172 out tokens · 45164 ms · 2026-05-14T22:03:33.501077+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    A. J. Liu and S. R. Nagel, Jamming is not just cool any more, Nature 396, 21 (1998)

    work page 1998

  2. [2]

    van Hecke, Jamming of soft particles: geometry, me- chanics, scaling and isostaticity, J

    M. van Hecke, Jamming of soft particles: geometry, me- chanics, scaling and isostaticity, J. Phys. Condens. Mat- ter 22, 033101 (2010)

    work page 2010

  3. [3]

    R. P. Behringer and B. Chakraborty, The physics of jam- ming for granular materials: a review, Rep. Prog. Phys. 82, 012601 (2019)

    work page 2019

  4. [4]

    C. S. O’Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Random packings of frictionless particles, Phys. Rev. Lett. 88, 075507 (2002)

    work page 2002

  5. [5]

    C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E 68, 011306 (2003)

    work page 2003

  6. [6]

    Wyart, On the rigidity of amorphous solids, Ann

    M. Wyart, On the rigidity of amorphous solids, Ann. Phys. 30, 1 (2005)

    work page 2005

  7. [7]

    Wyart, L

    M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Wit- ten, Effects of compression on the vibrational modes of marginally jammed solids, Phys. Rev. E 72, 051306 (2005)

    work page 2005

  8. [8]

    Otsuki and H

    M. Otsuki and H. Hayakawa, Discontinuous change of shear modulus for frictional jammed granular materials, Phys. Rev. E 95, 062902 (2017)

    work page 2017

  9. [9]

    Chaudhuri, L

    P. Chaudhuri, L. Berthier, and S. Sastry, Jamming tran- sitions in amorphous packings of frictionless spheres oc- cur over a continuous range of volume fractions, Phys. Rev. Lett. 104, 165701 (2010)

    work page 2010

  10. [10]

    Kumar and S

    N. Kumar and S. Luding, Memory of jamming-multiscale models for soft and granular matter, Granul. Matter 18, 58 (2016)

    work page 2016

  11. [11]

    V ˚ agberg, P

    D. V ˚ agberg, P. Olsson, and S. Teitel, Glassiness, rigidity, and jamming of frictionless soft core disks, Phys. Rev. E 83, 031307 (2011)

    work page 2011

  12. [12]

    Ozawa, T

    M. Ozawa, T. Kuroiwa, A. Ikeda, and K. Miyazaki, Jam- ming transition and inherent structures of hard spheres and disks, Physical Review Letters 109, 205701 (2012)

    work page 2012

  13. [13]

    Ozawa, L

    M. Ozawa, L. Berthier, and D. Coslovich, Exploring the jamming transition over a wide range of critical densities, SciPost Phys. 3, 027 (2017)

    work page 2017

  14. [14]

    Urbani and F

    P. Urbani and F. Zamponi, Shear yielding and shear jam- ming of dense hard sphere glasses, Phys. Rev. Lett. 118, 038001 (2017)

    work page 2017

  15. [15]

    Jin and H

    Y. Jin and H. Yoshino, A jamming plane of sphere pack- ings, Proc. Natl. Acad. Sci. U. S. A. 118, e2021794118 (2021)

    work page 2021

  16. [16]

    Kawasaki and K

    T. Kawasaki and K. Miyazaki, Unified understanding of nonlinear rheology near the jamming transition point, Phys. Rev. Lett. 132, 268201 (2024)

    work page 2024

  17. [17]

    D. Bi, J. Zhang, B. Chakraborty, and R. P. Behringer, Jamming by shear, Nature 480, 355 (2011)

    work page 2011

  18. [18]

    H. A. Vinutha and S. Sastry, Disentangling the role of structure and friction in shear jamming, Nat. Phys. 12, 578 (2016)

    work page 2016

  19. [19]

    Nagasawa, K

    K. Nagasawa, K. Miyazaki, and T. Kawasaki, Classifi- cation of the reversible–irreversible transitions in part i- cle trajectories across the jamming transition point, Soft Matter 15, 7557 (2019)

    work page 2019

  20. [20]

    Otsuki and H

    M. Otsuki and H. Hayakawa, Shear jamming, discontin- uous shear thickening, and fragile states in dry granu- lar materials under oscillatory shear, Phys. Rev. E 101, 032905 (2020)

    work page 2020

  21. [21]

    V. Babu, D. Pan, Y. Jin, B. Chakraborty, and S. Sastry, Dilatancy, shear jamming, and a generalized jamming phase diagram of frictionless sphere packings, Soft Matter 6 17, 3121 (2021)

    work page 2021

  22. [22]

    D. Pan, F. Meng, and Y. Jin, Shear hardening in fric- tionless amorphous solids near the jamming transition, PNAS Nexus 2, 1 (2023)

    work page 2023

  23. [23]

    D. Pan, Y. Wang, H. Yoshino, J. Zhang, and Y. Jin, A review on shear jamming, Phys. Rep. 1038, 1 (2023)

    work page 2023

  24. [24]

    Zheng, S

    W. Zheng, S. Zhang, and N. Xu, Jamming of packings of frictionless particles with and without shear, Chin. Phys. B 27, 066102 (2018)

    work page 2018

  25. [25]

    Zaccone and E

    A. Zaccone and E. Scossa-Romano, Approximate analyt- ical description of the nonaffine response of amorphous solids, Phys. Rev. B 83, 184205 (2011)

    work page 2011

  26. [26]

    B. P. Tighe, Relaxations and rheology near jamming, Phys. Rev. Lett. 107, 158303 (2011)

    work page 2011

  27. [27]

    Wyart, Scaling of phononic transport with connectiv - ity in amorphous solids, EPL 89, 64001 (2010)

    M. Wyart, Scaling of phononic transport with connectiv - ity in amorphous solids, EPL 89, 64001 (2010)

    work page 2010

  28. [28]

    Yoshino and F

    H. Yoshino and F. Zamponi, Shear modulus of glasses: Results from the full replica-symmetry-breaking solution , Phys. Rev. E 90, 022302 (2014)

    work page 2014

  29. [29]

    DeGiuli, E

    E. DeGiuli, E. Lerner, C. Brito, and M. Wyart, Force distribution affects vibrational properties in hard-spher e glasses, Proc. Natl. Acad. Sci. U. S. A. 111, 17054 (2014)

    work page 2014

  30. [30]

    DeGiuli, A

    E. DeGiuli, A. Laversanne-Finot, G. D¨ uring, E. Lerner , and M. Wyart, Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amor- phous solids, Soft Matter 10, 5628 (2014)

    work page 2014

  31. [31]

    X. Mao, N. Xu, and T. C. Lubensky, Soft modes and elasticity of nearly isostatic lattices: Randomness and dissipation, Phys. Rev. Lett. 104, 085504 (2010)

    work page 2010

  32. [32]

    Mizuno and A

    H. Mizuno and A. Ikeda, Effective medium theory for viscoelasticity of soft jammed solids, EPL 148, 36001 (2024)

    work page 2024

  33. [33]

    Ikeda and M

    H. Ikeda and M. Shimada, Vibrational density of states o f jammed packing at high dimensions: Mean-field theory, Phys. Rev. E 106, 024904 (2022)

    work page 2022

  34. [34]

    C. P. Goodrich, S. Dagois-Bohy, B. P. Tighe, M. van Hecke, A. J. Liu, and S. R. Nagel, Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling , Phys. Rev. E 90, 022138 (2014)

    work page 2014

  35. [35]

    Mitarai and F

    N. Mitarai and F. Nori, Wet granular materials, Adv. Phys. 55, 1 (2006)

    work page 2006

  36. [36]

    Herminghaus, Wet Granular Matter , Vol

    S. Herminghaus, Wet Granular Matter , Vol. 08 (WORLD SCIENTIFIC, 2023)

    work page 2023

  37. [37]

    D. A. Head, Well defined transition to gel-like aggregat es of attractive athermal particles, Eur. Phys. J. E 22, 151 (2007)

    work page 2007

  38. [38]

    Chaudhuri, L

    P. Chaudhuri, L. Berthier, and L. Bocquet, Inhomoge- neous shear flows in soft jammed materials with tunable attractive forces, Phys. Rev. E 85, 021503 (2012)

    work page 2012

  39. [39]

    Irani, P

    E. Irani, P. Chaudhuri, and C. Heussinger, Impact of attractive interactions on the rheology of dense athermal particles, Phys. Rev. Lett. 112, 188303 (2014)

    work page 2014

  40. [40]

    Irani, P

    E. Irani, P. Chaudhuri, and C. Heussinger, Athermal rhe - ology of weakly attractive soft particles, Phys. Rev. E 94, 052608 (2016)

    work page 2016

  41. [41]

    Katgert, B

    G. Katgert, B. P. Tighe, and M. V. Hecke, The jamming perspective on wet foams, Soft Matter 9, 9739 (2013)

    work page 2013

  42. [42]

    D. J. Koeze and B. P. Tighe, Sticky matters: Jamming and rigid cluster statistics with attractive particle inte r- actions, Phys. Rev. Lett. 121, 188002 (2018)

    work page 2018

  43. [43]

    D. J. Koeze, L. Hong, A. Kumar, and B. P. Tighe, Elas- ticity of jammed packings of sticky disks, Phys. Rev. Res. 2, 032047 (2020)

    work page 2020

  44. [44]

    G. Lois, J. Blawzdziewicz, and C. S. O’Hern, Jamming transition and new percolation universality classes in par - ticulate systems with attraction, Phys. Rev. Lett. 100, 028001 (2008)

    work page 2008

  45. [45]

    Yoshii and M

    K. Yoshii and M. Otsuki, Mechanical and geometrical properties of jammed weakly cohesive granular materials, J. Phys. Soc. Japan 94, 084801 (2025)

    work page 2025

  46. [46]

    Zheng, H

    W. Zheng, H. Liu, and N. Xu, Shear-induced solidifi- cation of athermal systems with weak attraction, Phys. Rev. E 94, 062608 (2016)

    work page 2016

  47. [47]

    S. Roy, A. Singh, S. Luding, and T. Weinhart, Mi- cro–macro transition and simplified contact models for wet granular materials, Comput. Part. Mech. 3, 449 (2016)

    work page 2016

  48. [48]

    See Supplemental Material for additional details of th e analysis and numerical results

    work page

  49. [49]

    P. A. Cundall and O. D. L. Strack, A discrete numeri- cal model for granular assemblies, G´ eotechnique 29, 47 (1979)

    work page 1979

  50. [50]

    Brito, E

    C. Brito, E. Lerner, and M. Wyart, Theory for swap ac- celeration near the glass and jamming transitions for con- tinuously polydisperse particles, Phys. Rev. X 8, 031050 (2018). 7 Supplemental Material: DETAILS OF NUMERICAL SIMULATIONS In our simulations, we consider N frictionless monodis- perse particles of mass m in a cubic box of size L. Particle dyn...

    work page 2018

  51. [51]

    0001, and 0

    0, 0 . 0001, and 0 . 001. The solid line represents the EMT prediction, Eq. (6) in the main text. SCALING PLOT FROM PRESSURE-CONTROLLED SIMULATIONS WITH DIFFERENT α To confirm that the generalized scaling relation is in- dependent of both the simulation protocol and the at- traction strength α , we performed additional simulations using a pressure-controll...

    work page