TY - JOUR

T1 - Jammed frictionless disks

T2 - connecting local and global response

AU - Ellenbroek, W.G.

AU - van Hecke, M.

AU - van Saarloos, W.

PY - 2009/12/29

Y1 - 2009/12/29

N2 - By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale ℓ* up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Δz, where Δz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli.

AB - By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale ℓ* up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Δz, where Δz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli.

UR - http://www.scopus.com/inward/record.url?scp=77149149423&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.061307

DO - 10.1103/PhysRevE.80.061307

M3 - Article

C2 - 20365168

AN - SCOPUS:77149149423

VL - 80

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 6

M1 - 061307

ER -