The fate of shear-oscillated amorphous solids.

The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subjected to athermal and quasi-static oscillatory deformations at various fixed amplitudes. The steady-state reached after several oscillations is fully determined by the initial preparation and the oscillation amplitude, as seen from stroboscopic stress and energy measurements. Under small oscillations, poorly annealed materials display shear-annealing, while ultra-stabilized materials are insensitive to them. Yet, beyond a critical oscillation amplitude, both kinds of materials display a discontinuous transition to the same mixed state composed of a fluid shear-band embedded in a marginal solid. Quantitative relations between uniform shear and the steady-state reached with this protocol are established. The transient regime characterizing the growth and the motion of the shear band is also studied.

Damage Accumulation in Silica Glass Nanofibers.

The origin of the brittle-to-ductile transition, experimentally observed in amorphous silica nanofibers as the sample size is reduced, is still debated. Here we investigate the issue by extensive molecular dynamics simulations at low and room temperatures for a broad range of sample sizes, with open and periodic boundary conditions. Our results show that small sample-size enhanced ductility is primarily due to diffuse damage accumulation, that for larger samples leads to brittle catastrophic failure. Surface effects such as boundary fluidization contribute to ductility at room temperature by promoting necking, but are not the main driver of the transition. Our results suggest that the experimentally observed size-induced ductility of silica nanofibers is a manifestation of finite-size criticality, as expected in general for quasi-brittle disordered networks.

Creep dynamics of athermal amorphous materials: a mesoscopic approach.

Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesoscale elasto-plastic descriptions to analyze such transient dynamics in athermal systems. Both our mean-field and space-dependent approaches consistently reproduce the typical experimental strain rate responses to different applied steps in stress. Moreover, they allow us to understand basic processes involved in the strain rate slowing down (creep) and the strain rate acceleration (fluidization) phases. The fluidization time increases in a power-law fashion as the applied external stress approaches a static yield stress. This stress value is related to the stress over-shoot in shear start-up experiments, and it is known to depend on sample preparation and age. By calculating correlations of the accumulated plasticity in the spatially resolved model, we reveal different modes of cooperative motion during the creep dynamics.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics.

In the presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps called avalanches, while, at much smaller fields, these interfaces creep by thermal activation. In this Letter, we develop a novel numerical technique that captures the ultraslow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatiotemporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assemble in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee these correlated dynamics being experimentally accessible by magnetooptical imaging of ferromagnetic films.

Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition.

We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elastoplastic model, we analyze system size and shear-rate dependence of the stress-drop duration and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving.

Edwards Thermodynamics for a Driven Athermal System with Dry Friction.

We obtain, using semianalytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear divergence of the correlation length as a function of energy density observed in direct numerical simulations of the model under tapping dynamics. We further characterize analytically this divergence using a Gaussian approximation for the distribution of mechanically stable configurations, and show that it is related to the existence of a peculiar infinite temperature critical point.

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-dimensional 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.

Properties of the density of shear transformations in driven amorphous solids.

The strain load Δγthat triggers consecutive avalanches is a key observable in the slow deformation of amorphous solids. Its temporally averaged value ⟨Δγ⟩ displays a non-trivial system-size dependence that constitutes one of the distinguishing features of the yielding transition. Details of this dependence are not yet fully understood. We address this problem by means of theoretical analysis and simulations of elastoplastic models for amorphous solids. An accurate determination of the size dependence of ⟨Δγ⟩ leads to a precise evaluation of the steady-state distribution of local distances to instabilityx. We find that the usually assumed formP(x) ∼xθ(withθbeing the so-called pseudo-gap exponent) is not accurate at lowxand that in generalP(x) tends to a system-size-dependentfinitelimit asx→ 0. We work out the consequences of this finite-size dependence standing on exact results for random-walks and disclosing an alternative interpretation of the mechanical noise felt by a reference site. We test our predictions in two- and three-dimensional elastoplastic models, showing the crucial influence of the saturation ofP(x) at smallxon the size dependence of ⟨Δγ⟩ and related scalings.

Nonequilibrium characterization of spinodal points using short time dynamics.

Although intuitively appealing, the concept of spinodal is rigorously defined only in systems with infinite range interactions (mean-field systems). In short-range systems, a pseudospinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean-field systems and with the pseudospinodal point obtained by extrapolation of metaequilibrium behavior in short-range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.

Magnetic domain wall creep and depinning: A scalar field model approach.

Magnetic domain wall motion is at the heart of new magnetoelectronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.

Long-term ordering kinetics of the two-dimensional q-state Potts model.

We studied the nonequilibrium dynamics of the q-state Potts model in the square lattice, after a quench to subcritical temperatures. By means of a continuous time Monte Carlo algorithm (nonconserved order parameter dynamics) we analyzed the long term behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different dynamical regimes, according to quench temperature range. At low (but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain growth behavior is interrupted with finite probability when the system gets stuck in highly symmetric nonequilibrium metastable states, which induce activation in the domain growth, in agreement with early predictions of Lifshitz [JETP 42, 1354 (1962)]. Moreover, if the temperature is very low, the system always gets stuck at short times in highly disordered metastable states with finite lifetime, which have been recently identified as glassy states. The finite size scaling properties of the different relaxation times involved, as well as their temperature dependency, are analyzed in detail.

Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids.

By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady-state plastic flow, focusing on systems with low internal dissipation. We analyze the distributions of avalanche sizes and durations and the density of shear transformations when varying the damping strength. In contrast to avalanches in the overdamped case, dominated by the yielding point universal exponents, inertial avalanches are controlled by a nonuniversal damping-dependent feedback mechanism, eventually turning negligible the role of correlations. Still, some general properties of avalanches persist and new scaling relations can be proposed.