Thermally activated flow in models of amorphous solids

Thermally activated intermittent flow in amorphous solids

Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate  and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.

Local vs. cooperative: Unraveling glass transition mechanisms with SEER

Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or "excitations" govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, Systematic Excitation ExtRaction, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.

Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Scaling Description of Creep Flow in Amorphous Solids

Amorphous solids such as coffee foam, toothpaste, or mayonnaise display a transient creep flow when a stress Σ is suddenly imposed. The associated strain rate is commonly found to decay in time as γ[over ˙]∼t^{-ν}, followed either by arrest or by a sudden fluidization. Various empirical laws have been suggested for the creep exponent ν and fluidization time τ_{f} in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between Σ and the transient yield stress Σ_{t}(γ) that characterizes the stability of configurations visited by the system at strain γ. Assuming the analyticity of Σ_{t}(γ) allows us to predict ν and asymptotic behaviors of τ_{f} in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.

Dynamic phase diagram of plastically deformed amorphous solids at finite temperature

The yielding transition that occurs in amorphous solids under athermal quasistatic deformation has been the subject of many theoretical and computational studies. Here, we extend this analysis to include thermal effects at finite shear rate, focusing on how temperature alters avalanches. We derive a nonequilibrium phase diagram capturing how temperature and strain rate effects compete, when avalanches overlap, and whether finite-size effects dominate over temperature effects. The predictions are tested through simulations of an elastoplastic model in two dimensions and in a mean-field approximation. We find a scaling for temperature-dependent softening in the low-strain rate regime when avalanches do not overlap, and a temperature-dependent Herschel-Bulkley exponent in the high-strain rate regime when avalanches do overlap.

Mean-Field Theory of Yielding under Oscillatory Shear

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.