122 research outputs found
Nontrivial rheological exponents in sheared yield stress fluids
In this work we discuss possible physical origins for non-trivial exponents
in the athermal rheology of soft materials at low but finite driving rates. A
key ingredient in our scenario is the presence of a self-consistent mechanical
noise that stems from the spatial superposition of long-range elastic responses
to localized plastically deforming regions. We study analytically a mean-field
model, in which this mechanical noise is accounted for by a stress diffusion
term coupled to the plastic activity. Within this description we show how a
dependence of the shear modulus and/or the local relaxation time on the shear
rate introduces corrections to the usual mean-field prediction, concerning the
Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the
mean-field picture is then shown to be robust with respect to structural
disorder and partial relaxation of the local stress. We test this prediction
numerically on a mesoscopic lattice model that implements explicitly the
long-range elastic response to localized shear transformations, and we conclude
on how our scenario might be tested in rheological experiments
Dependence of the fluctuation-dissipation temperature on the choice of observable
On general grounds, a nonequilibrium temperature can be consistently defined
from generalized fluctuation-dissipation relations only if it is independent of
the observable considered. We argue that the dependence on the choice of
observable generically occurs when the phase-space probability distribution is
non-uniform on constant energy shells. We relate quantitatively this observable
dependence to a fundamental characteristics of nonequilibrium systems, namely
the Shannon entropy difference with respect to the equilibrium state with the
same energy. This relation is illustrated on a mean-field model in contact with
two heat baths at different temperatures.Comment: 4 pages, 2 figures, final versio
Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature
We study the rheology of amorphous solids in the limit of negligible thermal
fluctuations. On the basis of general arguments, the flow curve is shown to
result from an interplay between the time scales of the macroscopic driving and
the (cascades of) local particle rearrangements. Such rearrangements are known
to induce a redistribution of the elastic stress in the system. Although
mechanical noise, i.e., the local stress fluctuations arising from this
redistribution, is widely believed to activate new particle rearrangements, we
provide evidence that casts severe doubt on the analogy with thermal
fluctuations: mechanical and thermal fluctuations lead to asymptotically
different statistics for barrier crossing. These ideas are illustrated and
supported by a simple coarse-grained model whose ingredients are directly
connected with the physical processes relevant for the flow.Comment: 6 pages, 3 figures + Supp. Ma
Mean-field scenario for the athermal creep dynamics of yield-stress fluids
We develop an elasto-plastic description for the transient dynamics prior to
steady flow of athermally yielding materials. Our mean-field model not only
reproduces the experimentally observed non-linear time dependence of the
shear-rate response to an external shear-stress, but also allows for the
determination of the different physical processes involved in the onset of the
re-acceleration phase after the initial critical slowing down and a distinct
well defined fluidization phase. The evidenced power-law dependence of the
fluidization time on the distance of the applied to an age dependent static
yield stress is not universal but strongly dependent on initial conditions.Comment: 8 pages, 4 figure
Criticality at finite strain rate in fluidized soft glassy materials
We study the emergence of critical dynamics in the steady shear rheology of
fluidized soft glassy materials. Within a mesoscale elasto-plastic model
accounting for a shear band instability, we show how an additional noise can
induce a transition from phase separated to homogeneous flow, accompanied by
critical-like fluctuations of the macroscopic shear rate. Both macroscopic
quantities and fluctuations exhibit power law behaviors in the vicinity of this
transition, consistent with previous experimental findings on vibrated granular
media. Altogether, our results suggest a generic scenario for the emergence of
criticality when shear weakening mechanisms compete with a fluidizing noise.Comment: 7 pages, 7 figure
Intensive thermodynamic parameters in nonequilibrium systems
Considering a broad class of steady-state nonequilibrium systems for which
some additive quantities are conserved by the dynamics, we introduce from a
statistical approach intensive thermodynamic parameters (ITPs) conjugated to
the conserved quantities. This definition does not require any detailed balance
relation to be fulfilled. Rather, the system has to satisfy a general
additivity property, which holds in most of the models usually considered in
the literature, including those described by a matrix product ansatz with
finite matrices. The main property of these ITPs is to take equal values in two
subsystems, making them a powerful tool to describe nonequilibrium phase
coexistence, as illustrated on different models. We finally discuss the issue
of the equalization of ITPs when two different systems are put into contact.
This issue is closely related to the possibility of measuring the ITPs using a
small auxiliary system, in the same way as temperature is measured with a
thermometer, and points at one of the major difficulties of nonequilibrium
statistical mechanics. In addition, an efficient alternative determination,
based on the measure of fluctuations, is also proposed and illustrated.Comment: 17 pages, 5 figures; final version, with minor change
Large Scale Parallelized 3d Mesoscopic Simulations of the Mechanical Response to Shear in Disordered Media
In this paper we describe the development of a code that implements a coarse grained dynamics for the large
scale modeleling of 3 dimensional athermal yielding and flow of disordered systems under externally applied
steady shear. The stochastic lattice model for the heterogeneous flow response involves long range elastic
interactions, that are resolved using fast Fourier techniques, implemented in parallel in an efficient and well
scaling MPI algorithm
Relaxation in yield stress systems through elastically interacting activated events
We study consequences of long-range elasticity in thermally assisted dynamics
of yield stress materials. Within a two-dimensinal mesoscopic model we
calculate the mean-square displacement and the dynamical structure factor for
tracer particle trajectories. The ballistic regime at short time scales is
associated with a compressed exponential decay in the dynamical structure
factor, followed by a subdiffusive crossover prior to the onset of diffusion.
We relate this crossover to spatiotemporal correlations and thus go beyond
established mean field predictions.Comment: 5 pages, 2 figures, to appear in PR
On the relevance of disorder in athermal amorphous materials under shear
We show that, at least at a mean-field level, the effect of structural
disorder in sheared amorphous media is very dissimilar depending on the thermal
or athermal nature of their underlying dynamics. We first introduce a toy
model, including explicitly two types of noise (thermal versus athermal).
Within this interpretation framework, we argue that mean-field athermal
dynamics can be accounted for by the so-called H{\'e}braud-Lequeux (HL) model,
in which the mechanical noise stems explicitly from the plastic activity in the
sheared medium. Then, we show that the inclusion of structural disorder, by
means of a distribution of yield energy barriers, has no qualitative effect in
the HL model, while such a disorder is known to be one of the key ingredients
leading kinematically to a finite macroscopic yield stress in other mean-field
descriptions, such as the Soft-Glassy-Rheology model. We conclude that the
statistical mechanisms at play in the emergence of a macroscopic yield stress,
and a complex stationary dynamics at low shear rate, are different in thermal
and athermal amorphous systems
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