Instabilities of Jammed Packings of Frictionless Spheres Under Load

Xu, Ning; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1103/PhysRevLett.119.215502

Instabilities of Jammed Packings of Frictionless Spheres Under Load

Journal Article · Mon Nov 20 00:00:00 EST 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.119.215502· OSTI ID:1596541

Xu, Ning ^[1]; Liu, Andrea J. ^[2]; Nagel, Sidney R. ^[3]

Univ. of Science and Technology of China, Hefei (China); University of Pennsylvania
Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Chicago, IL (United States). James Franck and Enrico Fermi Institutes

In this work, we consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as ω³ at low frequencies ω, and a contribution to the distribution of energy barriers ΔH that scales as ΔH^-1/3 at low barrier heights.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: Fundamental Research Funds for the Central Universities; National Natural Science Foundation; Simons Foundation; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: FG02-03ER46088; FG02-05ER46199

OSTI ID:: 1596541

Alternate ID(s):: OSTI ID: 1409469
OSTI ID: 1541246

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 21 Vol. 119; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (40)

Supercooled liquids and the glass transition Debenedetti, Pablo G.; Stillinger, Frank H. Nature, Vol. 410, Issue 6825 https://doi.org/10.1038/35065704	journal	March 2001
Fractal free energy landscapes in structural glasses Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4725	journal	April 2014
Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids DeGiuli, Eric; Laversanne-Finot, Adrien; Düring, Gustavo Soft Matter, Vol. 10, Issue 30 https://doi.org/10.1039/C4SM00561A	journal	January 2014
On the rigidity of amorphous solids Wyart, M. Annales de Physique, Vol. 30, Issue 3 https://doi.org/10.1051/anphys:2006003	journal	January 2005
Relationships of shear-induced changes in the potential energy landscape to the mechanical properties of ductile glasses Malandro, Dennis L.; Lacks, Daniel J. The Journal of Chemical Physics, Vol. 110, Issue 9 https://doi.org/10.1063/1.478340	journal	March 1999
Scaling description of the yielding transition in soft amorphous solids at zero temperature Lin, Jie; Lerner, Edan; Rosso, Alberto Proceedings of the National Academy of Sciences, Vol. 111, Issue 40 https://doi.org/10.1073/pnas.1406391111	journal	September 2014
Local thermal energy as a structural indicator in glasses Zylberg, Jacques; Lerner, Edan; Bar-Sinai, Yohai Proceedings of the National Academy of Sciences, Vol. 114, Issue 28 https://doi.org/10.1073/pnas.1704403114	journal	June 2017
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
The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential Altieri, Ada; Franz, Silvio; Parisi, Giorgio Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 9 https://doi.org/10.1088/1742-5468/2016/09/093301	journal	September 2016
Computer simulation of local order in condensed phases of silicon Stillinger, Frank H.; Weber, Thomas A. Physical Review B, Vol. 31, Issue 8 https://doi.org/10.1103/PhysRevB.31.5262	journal	April 1985
Bosonic excitations in random media Gurarie, V.; Chalker, J. T. Physical Review B, Vol. 68, Issue 13 https://doi.org/10.1103/PhysRevB.68.134207	journal	October 2003
Free-energy landscapes, dynamics, and the edge of chaos in mean-field models of spin glasses Aspelmeier, T.; Blythe, R. A.; Bray, A. J. Physical Review B, Vol. 74, Issue 18 https://doi.org/10.1103/PhysRevB.74.184411	journal	November 2006
Jamming at zero temperature and zero applied stress: The epitome of disorder O’Hern, Corey S.; Silbert, Leonardo E.; Liu, Andrea J. Physical Review E, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevE.68.011306	journal	July 2003
Amorphous systems in athermal, quasistatic shear Maloney, Craig E.; Lemaître, Anaël Physical Review E, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevE.74.016118	journal	July 2006
Heat transport in model jammed solids Vitelli, Vincenzo; Xu, Ning; Wyart, Matthieu Physical Review E, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevE.81.021301	journal	February 2010
Statistical physics of the yielding transition in amorphous solids Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar Physical Review E, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevE.82.055103	journal	November 2010
Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions Salerno, K. Michael; Robbins, Mark O. Physical Review E, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevE.88.062206	journal	December 2013
Nonlinear plastic modes in disordered solids Gartner, Luka; Lerner, Edan Physical Review E, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevE.93.011001	journal	January 2016
Echoes from anharmonic normal modes in model glasses Burton, Justin C.; Nagel, Sidney R. Physical Review E, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevE.93.032905	journal	March 2016
Micromechanics of nonlinear plastic modes Lerner, Edan Physical Review E, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevE.93.053004	journal	May 2016
Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses Lerner, Edan; Bouchbinder, Eran Physical Review E, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevE.96.020104	journal	August 2017
Vibrational Modes Identify Soft Spots in a Sheared Disordered Packing Manning, M. L.; Liu, A. J. Physical Review Letters, Vol. 107, Issue 10 https://doi.org/10.1103/PhysRevLett.107.108302	journal	August 2011
Soft-Sphere Packings at Finite Pressure but Unstable to Shear Dagois-Bohy, Simon; Tighe, Brian P.; Simon, Johannes Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.095703	journal	August 2012
Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior? Salerno, K. Michael; Maloney, Craig E.; Robbins, Mark O. Physical Review Letters, Vol. 109, Issue 10 https://doi.org/10.1103/PhysRevLett.109.105703	journal	September 2012
Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential Liu, Hao; Xie, Xiaoyi; Xu, Ning Physical Review Letters, Vol. 112, Issue 14 https://doi.org/10.1103/PhysRevLett.112.145502	journal	April 2014
Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods Cubuk, E. D.; Schoenholz, S. S.; Rieser, J. M. Physical Review Letters, Vol. 114, Issue 10 https://doi.org/10.1103/PhysRevLett.114.108001	journal	March 2015
Statistics and Properties of Low-Frequency Vibrational Modes in Structural Glasses Lerner, Edan; Düring, Gustavo; Bouchbinder, Eran Physical Review Letters, Vol. 117, Issue 3 https://doi.org/10.1103/PhysRevLett.117.035501	journal	July 2016
Universal Non-Debye Scaling in the Density of States of Amorphous Solids Charbonneau, Patrick; Corwin, Eric I.; Parisi, Giorgio Physical Review Letters, Vol. 117, Issue 4 https://doi.org/10.1103/PhysRevLett.117.045503	journal	July 2016
Phonon Echoes in Glass Golding, Brage; Graebner, John E. Physical Review Letters, Vol. 37, Issue 13 https://doi.org/10.1103/PhysRevLett.37.852	journal	September 1976
Molecular-Level Mechanical Instabilities and Enhanced Self-Diffusion in Flowing Liquids Malandro, Dennis L.; Lacks, Daniel J. Physical Review Letters, Vol. 81, Issue 25 https://doi.org/10.1103/PhysRevLett.81.5576	journal	December 1998
Numerical Study of Metastable States in Ising Spin Glasses Cavagna, Andrea; Giardina, Irene; Parisi, Giorgio Physical Review Letters, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevLett.92.120603	journal	March 2004
Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow Maloney, Craig; Lemaître, Anaël Physical Review Letters, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevLett.93.016001	journal	July 2004
Vibrations and Diverging Length Scales Near the Unjamming Transition Silbert, Leonardo E.; Liu, Andrea J.; Nagel, Sidney R. Physical Review Letters, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevLett.95.098301	journal	August 2005
Structural Relaxation Made Simple Bitzek, Erik; Koskinen, Pekka; Gähler, Franz Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.170201	journal	October 2006
Excess Vibrational Modes and the Boson Peak in Model Glasses Xu, Ning; Wyart, Matthieu; Liu, Andrea J. Physical Review Letters, Vol. 98, Issue 17 https://doi.org/10.1103/PhysRevLett.98.175502	journal	April 2007
Marginal Stability in Structural, Spin, and Electron Glasses Müller, Markus; Wyart, Matthieu Annual Review of Condensed Matter Physics, Vol. 6, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031214-014614	journal	March 2015
The Jamming Transition and the Marginally Jammed Solid Liu, Andrea J.; Nagel, Sidney R. Annual Review of Condensed Matter Physics, Vol. 1, Issue 1 https://doi.org/10.1146/annurev-conmatphys-070909-104045	journal	August 2010
On the density of shear transformations in amorphous solids Lin, Jie; Saade, Alaa; Lerner, Edan EPL (Europhysics Letters), Vol. 105, Issue 2 https://doi.org/10.1209/0295-5075/105/26003	journal	January 2014
Anharmonic and quasi-localized vibrations in jammed solids—Modes for mechanical failure Xu, N.; Vitelli, V.; Liu, A. J. EPL (Europhysics Letters), Vol. 90, Issue 5 https://doi.org/10.1209/0295-5075/90/56001	journal	June 2010
Nonlinear modes disentangle glassy and Goldstone modes in structural glasses Gartner, Luka; Lerner, Edan SciPost Physics, Vol. 1, Issue 2 https://doi.org/10.21468/SciPostPhys.1.2.016	journal	January 2016

Cited By (4)

Impact of jamming criticality on low-temperature anomalies in structural glasses Franz, Silvio; Maimbourg, Thibaud; Parisi, Giorgio Proceedings of the National Academy of Sciences, Vol. 116, Issue 28 https://doi.org/10.1073/pnas.1820360116	journal	June 2019
Theory for the density of interacting quasilocalized modes in amorphous solids Ji, Wencheng; Popović, Marko; de Geus, Tom W. J. Physical Review E, Vol. 99, Issue 2 https://doi.org/10.1103/physreve.99.023003	journal	February 2019
Theory for the density of interacting quasi-localised modes in amorphous solids Ji, Wencheng; Popović, Marko; de Geus, Tom W. J. arXiv https://doi.org/10.48550/arxiv.1806.01561	text	January 2018
Impact of jamming criticality on low-temperature anomalies in structural glasses Franz, Silvio; Maimbourg, Thibaud; Parisi, Giorgio arXiv https://doi.org/10.48550/arxiv.1811.11719	text	January 2018

Similar Records

Disordered surface vibrations in jammed sphere packings

Journal Article · Tue Feb 10 19:00:00 EST 2015 · Soft Matter · OSTI ID:1596345

Instabilities of Jammed Packings of Frictionless Spheres Under Load

Journal Article · Wed Nov 01 00:00:00 EDT 2017 · Physical Review Letters · OSTI ID:1541246

Emergent SO(₃) Symmetry of the Frictionless Shear Jamming Transition

Journal Article · Mon Jan 02 19:00:00 EST 2017 · Journal of Statistical Physics · OSTI ID:1596343

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
jamming
plasticity
shear

Instabilities of Jammed Packings of Frictionless Spheres Under Load

Citation Formats

References (40)

Cited By (4)

Similar Records

Related Subjects