We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are driven by power-law distributed mechanical noise from yield events throughout the material, in contrast to the well-studied Hébraud–Lequeux model where the noise is Gaussian. We first use a mapping to a mean first passage time problem to study the phase diagram in the absence of shear, which shows a transition between an arrested and a fluid state. We then introduce a boundary layer scaling technique for low yield rate regimes, which we first apply to study the scaling of the steady state yield rate on approaching the arrest transition. These scalings are further developed to study the aging behavior in the glassy regime for different values of the exponent μ characterizing the mechanical noise spectrum. We find that the yield rate decays as a power-law for 1 < μ < 2, a stretched exponential for μ = 1, and an exponential for μ < 1, reflecting the relative importance of far-field and near-field events as the range of the stress propagator is varied. A comparison of the mean-field predictions with aging simulations of a lattice elastoplastic model shows excellent quantitative agreement, up to a simple rescaling of time.
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December 2020
Research Article|
December 04 2020
Aging in a mean field elastoplastic model of amorphous solids
Special Collection:
Dynamics of Out-of-Equilibrium Soft Materials
Jack T. Parley
;
Jack T. Parley
a)
1
Institut für Theoretische Physik, University of Göttingen
, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
a)Author to whom correspondence should be addressed: jack.parley@uni-goettingen.de
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Suzanne M. Fielding
;
Suzanne M. Fielding
2
Science Laboratories, Department of Physics, Durham University
, South Road, Durham DH1 3LE, United Kingdom
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Peter Sollich
Peter Sollich
1
Institut für Theoretische Physik, University of Göttingen
, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
3
Department of Mathematics, King’s College London
, London WC2R 2LS, United Kingdom
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a)Author to whom correspondence should be addressed: jack.parley@uni-goettingen.de
Note: This paper is part of the Special Topic, Dynamics of Out-of-Equilibrium Soft Materials.
Physics of Fluids 32, 127104 (2020)
Article history
Received:
October 15 2020
Accepted:
November 13 2020
Citation
Jack T. Parley, Suzanne M. Fielding, Peter Sollich; Aging in a mean field elastoplastic model of amorphous solids. Physics of Fluids 1 December 2020; 32 (12): 127104. https://doi.org/10.1063/5.0033196
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