CONTENTSFrequently used notations 3 FIG. 1 Overview of amorphous solids. From left to right, top row : cellular phone case made of metallic glass (1); toothpaste (2); mayonnaise (3); coffee foam (4); soya beans (5). Second row : a transmission electron microscopy (TEM) image of a fractured bulk metallic glass (Cu50Zr45Ti5) by X. Tong et. al (Shanghai University, China); TEM image of blend (PLLA/PS) nanoparticles obtained by miniemulsion polymerization, from L. Becker Peres et al. (UFSC, Brazil); emulsion of water droplets in silicon oil observed with an optical microscope by N. Bremond (ESPCI Paris); a soap foam filmed in the lab by M. van Hecke (Leiden University, Netherlands); thin nylon cylinders of different diameters pictured with a camera, from T. Miller et al. (University of Sydney, Australia). The white scale bars are approximate. Just below, a chart of different amorphous materials, classified by the size and the damping regime of their elementary particles. At the bottom: some popular modeling approaches, arranged according to the length scales of the materials for which they were originally developed. STZ stands for the shear transformation zone theory of Langer (2008), and SGR for the soft glassy rheology theory of Sollich et al. (1997).

We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elasto-plastic model, we analyze size and shear-rate dependence of the stress-drop durations 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. 45.70.Ht, 63.50.Lm, 64.60.av Many materials respond to slow driving with strongly intermittent dynamics. Examples include Barkhausen noise in ferromagnets [1][2][3], stick-slip motion in earthquakes [4], serration dynamics in plasticity of solids [5], and avalanche dynamics in crack propagation [6,7], driven foams [8] and domain wall motion [9].As in equilibrium critical phenomena, global quantities linked to such bursting collective events are usually power law distributed and allow for the introduction of scaling functions. In the slow driving limit, the onset of motion can be interpreted as an out-of-equilibrium phase transition, suggesting the existence of families of systems that display similar avalanche statistics. To better identify this universality classes, both experimental [10-17] and theoretical [13,[18][19][20][21] works have discussed the avalanche "shapes", going beyond the study of scaling exponents.In deformation experiments of amorphous systems, such as grains, foams or metallic glasses, avalanche dynamics are typically evidenced in the time series of the deviatoric component of the stress tensor. In the limit of vanishing deformation rate we approach the so-called "yielding transition". The question whether yielding can be characterized as a continuous dynamical phase transition, belonging to a specific universality class, is still under debate. The analysis of avalanche statistics close to yielding has therefore a particular relevance.In this letter, we study the emerging yielding dynamics in a simple shear geometry with imposed driving rate. Our focus lies on the shear-rate dependence of the avalanche statistics and thus complement recent quasi-static studies [22][23][24][25], To address the low shear-rate regime we use a coarse-graining approach, proven to yield qualitative and quantitative relevant predictions [26][27][28][29][30][31], and compare the low shear-rate results of our meso-scale model with quasistatic particle-based simulations. Molecular dynamics (MD) -We consider a mixture of A and B particles interacting via a Lennard-Jones potential: V AB (r) = 4 AB [(σ AB /r) 12 − (σ AB /r) 6 ] with r being the distance between two particles. Units of energy, length and mass are defined by AA , σ AA and m A ; the unit of time is given by τ 0 = σ AA (m A / AA ). The potential is truncated at R c = 2.5 and a force smoothing is applied between an inner cut-off R in = 2.2 and R c . The two species of particles have equal mass m, but...