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Relationships between structure, memory and flow in sheared disordered materials


A fundamental challenge regarding disordered solids is predicting macroscopic yield—the point at which elastic behaviour changes to plastic behaviour—from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic rearrangements. This suggests that one path to understanding bulk rheology is to map particle configurations to their mode of deformation. Here, we subject two-dimensional dense colloidal systems to oscillatory shear, measure the particle trajectories and bulk rheology, and quantify particle microstructure using excess entropy. Our results reveal a direct relation between excess entropy and energy dissipation that is insensitive to the nature of interactions amongst particles. We use this relation to build a physically informed model that connects rheology to microstructure. Our findings suggest a framework for tailoring the rheological response of disordered materials by tuning microstructural properties.

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Fig. 1: Overview of structure, dynamics and response.
Fig. 2: Memory within microstructure.
Fig. 3: Entropy and material memories.
Fig. 4: Comparisons of imposed force, microstructural excess entropy and bulk rheology.

Data availability

Source data are provided with this paper. All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.


  1. Nagel, S. R. Experimental soft-matter science. Rev. Mod. Phys. 89, 025002 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  2. Ioannidou, K. et al. Mesoscale texture of cement hydrates. Proc. Natl Acad. Sci. U. S. A. 113, 2029–2034 (2016).

    ADS  Article  Google Scholar 

  3. Jerolmack, D. J. & Daniels, K. E. Viewing Earth’s surface as a soft-matter landscape. Nat. Rev. Phys. 1, 716–730 (2019).

    Article  Google Scholar 

  4. Nie, S., Jiang, Q., Cui, L. & Zhang, C. Investigation on solid–liquid transition of soft mud under steady and oscillatory shear loads. Sediment. Geol. 397, 105570 (2020).

    Article  Google Scholar 

  5. Falk, M. L. & Langer, J. S. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57, 7192–7205 (1998).

    ADS  Article  Google Scholar 

  6. Buttinoni, I. et al. Colloidal polycrystalline monolayers under oscillatory shear. Phys. Rev. E 95, 012610 (2017).

    ADS  Article  Google Scholar 

  7. Guazzelli, l & Pouliquen, O. Rheology of dense granular suspensions. J. Fluid Mech. 852, P1 (2018).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  8. Cipelletti, L., Martens, K. & Ramos, L. Microscopic precursors of failure in soft matter. Soft Matter 16, 82–93 (2020).

    ADS  Article  Google Scholar 

  9. Richard, D. et al. Predicting plasticity in disordered solids from structural indicators. Phys. Rev. Mater. 4, 113609 (2020).

    Article  Google Scholar 

  10. Galloway, K. L. et al. Scaling of relaxation and excess entropy in plastically deformed amorphous solids. Proc. Natl Acad. Sci. U. S. A. 117, 11887–11893 (2020).

    MathSciNet  Article  Google Scholar 

  11. Ingebrigtsen, T. S. & Tanaka, H. Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids. Proc. Natl Acad. Sci. U. S. A. 115, 87–92 (2018).

    ADS  Article  Google Scholar 

  12. Bonnecaze, R. T., Khabaz, F., Mohan, L. & Cloitre, M. Excess entropy scaling for soft particle glasses. J. Rheol. 64, 423–431 (2020).

    ADS  Article  Google Scholar 

  13. Dyre, J. C. Perspective: excess-entropy scaling. J. Chem. Phys. 149, 210901 (2018).

    ADS  Article  Google Scholar 

  14. Separdar, L., Bailey, N. P., Schrøder, T. B., Davatolhagh, S. & Dyre, J. C. Isomorph invariance of couette shear flows simulated by the sllod equations of motion. J. Chem. Phys. 138, 154505 (2013).

    ADS  Article  Google Scholar 

  15. Xia, X. & Wolynes, P. G. Fragilities of liquids predicted from the random first order transition theory of glasses. Proc. Natl Acad. Sci. U. S. A. 97, 2990–2994 (2000).

    ADS  Article  Google Scholar 

  16. Hallett, J. E., Turci, F. & Royall, C. P. Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations. Nat. Commun. 9, 1–10 (2018).

    Article  Google Scholar 

  17. Argon, A. Plastic deformation in metallic glasses. Acta Metal. 27, 47 – 58 (1979).

    Article  Google Scholar 

  18. Siebenbürger, M., Fuchs, M., Winter, H. & Ballauff, M. Viscoelasticity and shear flow of concentrated, noncrystallizing colloidal suspensions: comparison with mode-coupling theory. J. Rheol. 53, 707–726 (2009).

    ADS  Article  Google Scholar 

  19. Slotterback, S. et al. Onset of irreversibility in cyclic shear of granular packings. Phys. Rev. E 85, 021309 (2012).

    ADS  Article  Google Scholar 

  20. Cubuk, E. D. et al. Structure-property relationships from universal signatures of plasticity in disordered solids. Science 358, 1033–1037 (2017).

    ADS  Article  Google Scholar 

  21. Chen, K. et al. Low-frequency vibrations of soft colloidal glasses. Phys. Rev. Lett. 105, 025501 (2010).

    ADS  Article  Google Scholar 

  22. Xu, N., Wyart, M., Liu, A. J. & Nagel, S. R. Excess vibrational modes and the boson peak in model glasses. Phys. Rev. Lett. 98, 175502 (2007).

    ADS  Article  Google Scholar 

  23. Patinet, S., Vandembroucq, D. & Falk, M. L. Connecting local yield stresses with plastic activity in amorphous solids. Phys. Rev. Lett. 117, 045501 (2016).

    ADS  Article  Google Scholar 

  24. Patinet, S., Barbot, A., Lerbinger, M., Vandembroucq, D. & Lemaitre, A. Origin of the Bauschinger effect in amorphous solids. Phys. Rev. Lett. 124, 205503 (2020).

    ADS  Article  Google Scholar 

  25. Maestro, A. & Zaccone, A. Nonaffine deformation and tunable yielding of colloidal assemblies at the air–water interface. Nanoscale 9, 18343–18351 (2017).

    Article  Google Scholar 

  26. Bouchbinder, E. & Langer, J. S. Shear-transformation-zone theory of linear glassy dynamics. Phys. Rev. E 83, 061503 (2011).

    ADS  Article  Google Scholar 

  27. Keim, N. C. & Nagel, S. R. Generic transient memory formation in disordered systems with noise. Phys. Rev. Lett. 107, 010603 (2011).

    ADS  Article  Google Scholar 

  28. Mukherji, S., Kandula, N., Sood, A. & Ganapathy, R. Strength of mechanical memories is maximal at the yield point of a soft glass. Phys. Rev. Lett. (2019).

  29. Pashine, N., Hexner, D., Liu, A. J. & Nagel, S. R. Directed aging, memory, and nature’s greed. Sci. Adv. (2019).

  30. Keim, N. C., Hass, J., Kroger, B. & Wieker, D. Global memory from local hysteresis in an amorphous solid. Phys. Rev. Res. 2, 012004 (2020).

    Article  Google Scholar 

  31. Gadala-Maria, F. & Acrivos, A. Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799–814 (1980).

    ADS  Article  Google Scholar 

  32. Keim, N. C., Paulsen, J. D. & Nagel, S. R. Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticity. Phys. Rev. E 88, 032306 (2013).

    ADS  Article  Google Scholar 

  33. Keim, N. C. & Arratia, P. E. Yielding and microstructure in a 2d jammed material under shear deformation. Soft Matter 9, 6222–6225 (2013).

    ADS  Article  Google Scholar 

  34. Teich, E. G., Galloway, K. L., Arratia, P. E. & Bassett, D. S. Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear. Sci. Adv. (2021).

  35. Keim, N. C. & Arratia, P. E. Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material. Phys. Rev. Lett. 112, 028302 (2014).

    ADS  Article  Google Scholar 

  36. Lundberg, M., Krishan, K., Xu, N., O’Hern, C. S. & Dennin, M. Reversible plastic events in amorphous materials. Phys. Rev. E 77, 041505 (2008).

    ADS  Article  Google Scholar 

  37. Möbius, R. & Heussinger, C. (ir)reversibility in dense granular systems driven by oscillating forces. Soft Matter 10, 4806–4812 (2014).

    ADS  Article  Google Scholar 

  38. Regev, I., Lookman, T. & Reichhardt, C. Onset of irreversibility and chaos in amorphous solids under periodic shear. Phys. Rev. E 88, 062401 (2013).

    ADS  Article  Google Scholar 

  39. van Hecke, M. Jamming of soft particles: geometry, mechanics, scaling and isostaticity. J. Phys. Condens. 22, 033101 (2009).

    Article  Google Scholar 

  40. Behringer, R. & Chakraborty, B. The physics of jamming for granular materials: a review. Rep. Prog. Phys. 82, 012601 (2018).

    ADS  Article  Google Scholar 

  41. Liu, A. J. & Nagel, S. R. The jamming transition and the marginally jammed solid. Annu. Rev. Condens. Matter Phys. 1, 347–369 (2010).

    ADS  Article  Google Scholar 

  42. Martinez, L. & Angell, C. A. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663–667 (2001).

    ADS  Article  Google Scholar 

  43. Vermant, J. & Solomon, M. J. Flow-induced structure in colloidal suspensions. J. Phys. Condens. 17, R187–R216 (2005).

    ADS  Article  Google Scholar 

  44. Cheng, X., McCoy, J. H., Israelachvili, J. N. & Cohen, I. Imaging the microscopic structure of shear thinning and thickening colloidal suspensions. Science 333, 1276–1279 (2011).

    ADS  Article  Google Scholar 

  45. Seth, J. R., Mohan, L., Locatelli-Champagne, C., Cloitre, M. & Bonnecaze, R. T. A micromechanical model to predict the flow of soft particle glasses. Nat. Mater. 10, 838–843 (2011).

    ADS  Article  Google Scholar 

  46. Parsi, F. & Gadala-Maria, F. Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J. Rheol. 31, 725–732 (1987).

    ADS  Article  Google Scholar 

  47. Dudowicz, J., Freed, K. F. & Douglas, J. F. Generalized Entropy Theory of Polymer Glass Formation (Wiley, 2007).

  48. Bi, D., Henkes, S., Daniels, K. E. & Chakraborty, B. The statistical physics of athermal materials. Annu. Rev. Condens. Matter Phys. 6, 63–83 (2015).

    ADS  Article  Google Scholar 

  49. Ono, I. K. et al. Effective temperatures of a driven system near jamming. Phys. Rev. Lett. 89, 095703 (2002).

    ADS  Article  Google Scholar 

  50. Khabaz, F. & Bonnecaze, R. T. Thermodynamics of shear-induced phase transition of polydisperse soft particle glasses. Phys. Fluids 33, 013315 (2021).

    ADS  Article  Google Scholar 

  51. Shahin, G. The Stress Deformation Interfacial Rheometer. Ph.D. thesis, University of Pennsylvania (1986).

  52. Brooks, C. F., Fuller, G. G., Frank, C. W. & Robertson, C. R. An interfacial stress rheometer to study rheological transitions in monolayers at the air/water interface. Langmuir 15, 2450–2459 (1999).

    Article  Google Scholar 

  53. Reynaert, S., Brooks, C. F., Moldenaers, P., Vermant, J. & Fuller, G. G. Analysis of the magnetic rod interfacial stress rheometer. J. Rheol. 52, 261–285 (2008).

    ADS  Article  Google Scholar 

  54. Aveyard, R., Clint, J. H., Nees, D. & Paunov, V. N. Compression and structure of monolayers of charged latex particles at air/water and octane/water interfaces. Langmuir 16, 1969–1979 (2000).

    Article  Google Scholar 

  55. Masschaele, K., Park, B. J., Furst, E. M., Fransaer, J. & Vermant, J. Finite ion-size effects dominate the interaction between charged colloidal particles at an oil–water interface. Phys. Rev. Lett. 105, 048303 (2010).

    ADS  Article  Google Scholar 

  56. Park, B. J., Vermant, J. & Furst, E. M. Heterogeneity of the electrostatic repulsion between colloids at the oil–water interface. Soft Matter 6, 5327–5333 (2010).

    ADS  Article  Google Scholar 

  57. Keim, N. C. & Arratia, P. E. Role of disorder in finite-amplitude shear of a 2D jammed material. Soft Matter 11, 1539–1546 (2015).

    ADS  Article  Google Scholar 

  58. Larson, R. The Structure and Rheology of Complex Fluids (Oxford Univ. Press, 2010).

  59. Baranyai, A. & Evans, D. J. Direct entropy calculation from computer simulation of liquids. Phys. Rev. A 40, 3817–3822 (1989).

    ADS  Article  Google Scholar 

  60. Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics (Sandia National Labs, 1993).

  61. Widom, M., Strandburg, K. J. & Swendsen, R. H. Quasicrystal equilibrium state. Phys. Rev. Lett. 58, 706 (1987).

    ADS  Article  Google Scholar 

  62. Glaser, J. et al. Strong scaling of general-purpose molecular dynamics simulations on gpus. Comput. Phys. Commun. 192, 97–107 (2015).

    Article  Google Scholar 

  63. Anderson, J. A., C. D., L. & Travesset, A. General purpose molecular dynamics simulations fully implemented on graphics processing units. J. Comput. Phys. 227, 5342–5359 (2008).

    ADS  MATH  Article  Google Scholar 

  64. Bitzek, E., Koskinen, P., Gähler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Phys. Rev. Lett. 97, 170201 (2006).

    ADS  Article  Google Scholar 

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We thank D. Durian, A. Liu, R. Riggleman, I. Regev and S. Kosgodagan Acharige for fruitful discussions. We especially thank A. Liu and R. Riggleman for the generous contribution of computational resources for our simulations. This work is partially funded by University of Pennsylvania’s MRSEC NSF-DMR-1720530 (K.L.G., E.G.T., X.G.M., Ch.K., I.R.G., D.J.J., A.G.Y. and P.E.A.) and by ARO W911-NF-16-1-0290 (K.L.G., D.J.J. and P.E.A.) and by NSF-DMR-2003659 (A.G.Y., X.G.M.). C.R. further thanks the NSF for career award CMMI-2047506.

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D.J.J., A.G.Y. and P.E.A. designed the research. K.L.G. and N.C.K. conducted the experiments. Ch.K. and I.R.G. ran the simulations. The analysis and model were developed by K.L.G., C.R., X.G.M., A.G.Y. and P.E.A. All authors discussed the results and wrote the manuscript.

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Correspondence to P. E. Arratia.

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Nature Physics thanks Francesco Turci and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Radial distribution function, g(x,y,t), accompanying Fig. 2a.

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Galloway, K.L., Teich, E.G., Ma, X.G. et al. Relationships between structure, memory and flow in sheared disordered materials. Nat. Phys. 18, 565–570 (2022).

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