Abstract
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 [J. Lin and M. 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 behaviour 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. 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.
| Original language | English |
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| Journal | PHYSICS OF FLUIDS |
| Publication status | Accepted/In press - 18 Nov 2020 |