[en] The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical microrheological
experiments.
Disciplines :
Physics
Author, co-author :
Ekeh, Timothy; DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
Fodor, Etienne ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Fielding, Suzanne M.; Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
Cates, Michael E.; DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
External co-authors :
yes
Language :
English
Title :
Power fluctuations in sheared amorphous materials: A minimal model
L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys. 83, 587 (2011) RMPHAT 0034-6861 10.1103/RevModPhys.83.587.
D. Bonn, M. M. Denn, L. Berthier, T. Divoux, and S. Manneville, Yield stress materials in soft condensed matter, Rev. Mod. Phys. 89, 035005 (2017) RMPHAT 0034-6861 10.1103/RevModPhys.89.035005.
A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat, Deformation and flow of amorphous solids: Insights from elastoplastic models, Rev. Mod. Phys. 90, 045006 (2018) RMPHAT 0034-6861 10.1103/RevModPhys.90.045006.
J. D. Martin and Y. T. Hu, Transient and steady-state shear banding in aging soft glassy materials, Soft Matter 8, 6940 (2012) 1744-683X 10.1039/c2sm25299f.
P. Coussot, Q. D. Nguyen, H. T. Huynh, and D. Bonn, Avalanche Behavior in Yield Stress Fluids, Phys. Rev. Lett. 88, 175501 (2002) PRLTAO 0031-9007 10.1103/PhysRevLett.88.175501.
J. Paredes, N. Shahidzadeh-Bonn, and D. Bonn, Shear banding in thixotropic and normal emulsions, J. Phys.: Condens. Matter 23, 284116 (2011) JCOMEL 0953-8984 10.1088/0953-8984/23/28/284116.
J. S. Langer, Shear-transformation-zone theory of yielding in athermal amorphous materials, Phys. Rev. E 92, 012318 (2015) PLEEE8 1539-3755 10.1103/PhysRevE.92.012318.
D. Lootens, H. Van Damme, and P. Hébraud, Giant Stress Fluctuations at the Jamming Transition, Phys. Rev. Lett. 90, 178301 (2003) PRLTAO 0031-9007 10.1103/PhysRevLett.90.178301.
P. Jop, V. Mansard, P. Chaudhuri, L. Bocquet, and A. Colin, Microscale Rheology of a Soft Glassy Material Close to Yielding, Phys. Rev. Lett. 108, 148301 (2012) PRLTAO 0031-9007 10.1103/PhysRevLett.108.148301.
A. L. Thomas, Z. Tang, K. E. Daniels, and N. M. Vriend, Force fluctuations at the transition from quasi-static to inertial granular flow, Soft Matter 15, 8532 (2019) 1744-683X 10.1039/C9SM01111K.
C. Liu, E. E. Ferrero, F. Puosi, J.-L. Barrat, and K. Martens, Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition, Phys. Rev. Lett. 116, 065501 (2016) PRLTAO 0031-9007 10.1103/PhysRevLett.116.065501.
A. Ninarello, L. Berthier, and D. Coslovich, Models and Algorithms for the Next Generation of Glass Transition Studies, Phys. Rev. X 7, 021039 (2017) 2160-3308 10.1103/PhysRevX.7.021039.
M. Ozawa, L. Berthier, G. Biroli, A. Rosso, and G. Tarjus, Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl. Acad. Sci. USA 115, 6656 (2018) PNASA6 0027-8424 10.1073/pnas.1806156115.
L. Berthier, E. Flenner, C. J. Fullerton, C. Scalliet, and M. Singh, Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids, J. Stat. Mech. (2019), 064004 1742-5468 10.1088/1742-5468/ab1910.
M. Ozawa, L. Berthier, G. Biroli, and G. Tarjus, Role of fluctuations in the yielding transition of two-dimensional glasses, Phys. Rev. Research 2, 023203 (2020) 2643-1564 10.1103/PhysRevResearch.2.023203.
M. Ozawa, L. Berthier, G. Biroli, and G. Tarjus, Rare events and disorder control the brittle yielding of amorphous solids, arXiv:2102.05846.
B. Miller, C. O'Hern, and R. P. Behringer, Stress Fluctuations for Continuously Sheared Granular Materials, Phys. Rev. Lett. 77, 3110 (1996) PRLTAO 0031-9007 10.1103/PhysRevLett.77.3110.
E. D. Knowlton, D. J. Pine, and L. Cipelletti, A microscopic view of the yielding transition in concentrated emulsions, Soft Matter 10, 6931 (2014) 1744-683X 10.1039/C4SM00531G.
K. W. Desmond and E. R. Weeks, Measurement of Stress Redistribution in Flowing Emulsions, Phys. Rev. Lett. 115, 098302 (2015) PRLTAO 0031-9007 10.1103/PhysRevLett.115.098302.
V. Chikkadi, G. Wegdam, D. Bonn, B. Nienhuis, and P. Schall, Long-Range Strain Correlations in Sheared Colloidal Glasses, Phys. Rev. Lett. 107, 198303 (2011) PRLTAO 0031-9007 10.1103/PhysRevLett.107.198303.
J. Zheng, A. Sun, Y. Wang, and J. Zhang, Energy Fluctuations in Slowly Sheared Granular Materials, Phys. Rev. Lett. 121, 248001 (2018) PRLTAO 0031-9007 10.1103/PhysRevLett.121.248001.
U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012) RPPHAG 0034-4885 10.1088/0034-4885/75/12/126001.
P. Hébraud and F. Lequeux, Mode-Coupling Theory for the Pasty Rheology of Soft Glassy Materials, Phys. Rev. Lett. 81, 2934 (1998) PRLTAO 0031-9007 10.1103/PhysRevLett.81.2934.
P. Sollich, F. Lequeux, P. Hébraud, and M. E. Cates, Rheology of Soft Glassy Materials, Phys. Rev. Lett. 78, 2020 (1997) PRLTAO 0031-9007 10.1103/PhysRevLett.78.2020.
S. H. E. Rahbari, A. A. Saberi, H. Park, and J. Vollmer, Characterizing rare fluctuations in soft particulate flows, Nat. Commun. 8, 11 (2017) 2041-1723 10.1038/s41467-017-00022-8.
E. Agoritsas, E. Bertin, K. Martens, and J.-L. Barrat, On the relevance of disorder in athermal amorphous materials under shear, Eur. Phys. J. E 38, 71 (2015) EPJSFH 1292-8941 10.1140/epje/i2015-15071-x.
L. Bocquet, A. Colin, and A. Ajdari, A Kinetic Theory of Plastic Flow in Soft Glassy Materials, Phys. Rev. Lett. 103, 036001 (2009) PRLTAO 0031-9007 10.1103/PhysRevLett.103.036001.
J. T. Parley, S. M. Fielding, and P. Sollich, Aging in a mean field elastoplastic model of amorphous solids, Phys. Fluids 32, 127104 (2020) PHFLE6 1070-6631 10.1063/5.0033196.
M. Popović, T. W. J. de Geus, and M. Wyart, Elastoplastic description of sudden failure in athermal amorphous materials during quasistatic loading, Phys. Rev. E 98, 040901 (R) (2018) 2470-0045 10.1103/PhysRevE.98.040901.
J. Lin, A. Saade, E. Lerner, A. Rosso, and M. Wyart, On the density of shear transformations in amorphous solids, Europhys. Lett. 105, 26003 (2014) EULEEJ 0295-5075 10.1209/0295-5075/105/26003.
A. Nicolas, K. Martens, and J.-L. Barrat, Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature, Europhys. Lett. 107, 44003 (2014) EULEEJ 0295-5075 10.1209/0295-5075/107/44003.
M. L. Goff, E. Bertin, and K. Martens, Giant fluctuations in the flow of fluidised soft glassy materials: An elasto-plastic modelling approach, J. Phys.: Mater. 3, 025010 (2020) 2515-7639 10.1088/2515-7639/ab6e46.
G. Picard, A. Ajdari, F. Lequeux, and L. Bocquet, Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids, Eur. Phys. J. E 15, 371 (2004) EPJSFH 1292-8941 10.1140/epje/i2004-10054-8.
J. Lin and M. Wyart, Mean-Field Description of Plastic Flow in Amorphous Solids, Phys. Rev. X 6, 011005 (2016) 2160-3308 10.1103/PhysRevX.6.011005.
A. Tanguy, F. Leonforte, and J.-L. Barrat, Plastic response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain rate, Eur. Phys. J. E 20, 355 (2006) EPJSFH 1292-8941 10.1140/epje/i2006-10024-2.
M. L. Falk and J. S. Langer, Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E 57, 7192 (1998) 1063-651X 10.1103/PhysRevE.57.7192.
C. E. Maloney and A. Lemaître, Amorphous systems in athermal, quasistatic shear, Phys. Rev. E 74, 016118 (2006) PLEEE8 1539-3755 10.1103/PhysRevE.74.016118.
A. Lemaître and C. Caroli, Plastic response of a two-dimensional amorphous solid to quasistatic shear: Transverse particle diffusion and phenomenology of dissipative events, Phys. Rev. E 76, 036104 (2007) PLEEE8 1539-3755 10.1103/PhysRevE.76.036104.
K. M. Salerno and M. O. Robbins, Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions, Phys. Rev. E 88, 062206 (2013) PLEEE8 1539-3755 10.1103/PhysRevE.88.062206.
J. Kurchan, Fluctuation theorem for stochastic dynamics, J. Phys. A: Math. Gen. 31, 3719 (1998) JPHAC5 0305-4470 10.1088/0305-4470/31/16/003.
C. Maes, The fluctuation theorem as a Gibbs property, J. Stat. Phys. 95, 367 (1999) JSTPBS 0022-4715 10.1023/A:1004541830999.
J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, J. Stat. Phys. 95, 333 (1999) JSTPBS 0022-4715 10.1023/A:1004589714161.
M. Esposito and C. Van den Broeck, Three Detailed Fluctuation Theorems, Phys. Rev. Lett. 104, 090601 (2010) PRLTAO 0031-9007 10.1103/PhysRevLett.104.090601.
S. M. Fielding, M. E. Cates, and P. Sollich, Shear banding, aging and noise dynamics in soft glassy materials, Soft Matter 5, 2378 (2009) 1744-683X 10.1039/B812394M.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.105.L052601 for details on analytical derivations and numerical simulations.
H. J. Barlow, J. O. Cochran, and S. M. Fielding, Ductile and Brittle Yielding in Thermal and Athermal Amorphous Materials, Phys. Rev. Lett. 125, 168003 (2020) PRLTAO 0031-9007 10.1103/PhysRevLett.125.168003.
C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer Series in Synergetics Vol. 13, 3rd ed. (Springer, Berlin, 2004).
D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Probability of Second Law Violations in Shearing Steady States, Phys. Rev. Lett. 71, 2401 (1993) PRLTAO 0031-9007 10.1103/PhysRevLett.71.2401.
G. Gallavotti and E. G. D. Cohen, Dynamical Ensembles in Nonequilibrium Statistical Mechanics, Phys. Rev. Lett. 74, 2694 (1995) PRLTAO 0031-9007 10.1103/PhysRevLett.74.2694.
S. Aumaître, S. Fauve, S. McNamara, and P. Poggi, Power injected in dissipative systems and the fluctuation theorem, Eur. Phys. J. B 19, 449 (2001) EPJBFY 1434-6028 10.1007/s100510170321.
J. Farago, Injected power fluctuations in Langevin equation, J. Stat. Phys. 107, 781 (2002) JSTPBS 0022-4715 10.1023/A:1014538214117.
K. Feitosa and N. Menon, Fluidized Granular Medium as an Instance of the Fluctuation Theorem, Phys. Rev. Lett. 92, 164301 (2004) PRLTAO 0031-9007 10.1103/PhysRevLett.92.164301.
A. Puglisi, P. Visco, A. Barrat, E. Trizac, and F. van Wijland, Fluctuations of Internal Energy Flow in a Vibrated Granular Gas, Phys. Rev. Lett. 95, 110202 (2005) PRLTAO 0031-9007 10.1103/PhysRevLett.95.110202.
L. F. Cugliandolo, The effective temperature, J. Phys. A: Math. Theor. 44, 483001 (2011) 1751-8113 10.1088/1751-8113/44/48/483001.
T. Ekeh (unpublished).
M. L. Falk and J. S. Langer, Deformation and failure of amorphous, solidlike materials, Annu. Rev. Condens. Matter Phys. 2, 353 (2011) 1947-5454 10.1146/annurev-conmatphys-062910-140452.
O. Sedes, A. Singh, and J. F. Morris, Fluctuations at the onset of discontinuous shear thickening in a suspension, J. Rheol. 64, 309 (2020) JORHD2 0148-6055 10.1122/1.5131740.
