Direct evidence of plastic events and dynamic heterogeneities in soft-glasses

By using fluid-kinetic simulations of confined and concentrated emulsion droplets, we investigate the nature of space non-homogeneity in soft-glassy dynamics and provide quantitative measurements of the statistical features of plastic events in the proximity of the yield-stress threshold. Above the yield stress, our results show the existence of a finite stress correlation scale, which can be mapped directly onto the {\it cooperativity scale}, recently introduced in the literature to capture non-local effects in the soft-glassy dynamics. In this regime, the emergence of a separate boundary (wall) rheology with higher fluidity than the bulk, is highlighted in terms of near-wall spontaneous segregation of plastic events. Near the yield stress, where the cooperative scale cannot be estimated with sufficient accuracy, the system shows a clear increase of the stress correlation scale, whereas plastic events exhibit intermittent clustering in time, with no preferential spatial location. A quantitative measurement of the space-time correlation associated with the motion of the interface of the droplets is key to spot the long-range amorphous order at the yield stress threshold

Modeling the mechanics of amorphous solids at different length and time scales

We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review studies based on atomistic simulations, with a particular emphasis on the role of the potential energy landscape and of the temperature. At the micrometer scale, we present the different mesoscopic models of amorphous plasticity and show the relation between shear banding and the type of disorder and correlations (e.g. elastic) included in the models. At the macroscopic range, we review the different constitutive laws used in finite element simulations. We end the review by a critical discussion on the opportunities and challenges offered by multiscale modeling and transfer of information between scales to study amorphous plasticity.Comment: 58 pages, 14 figure

Amorphous Systems in Athermal, Quasistatic Shear

We present results on a series of 2D atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events. The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix. The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed. Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear -- so-called "shear bands" -- found in related studies. The slip lines gives rise to particular scalings with system length of various measures of event size. Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions. The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials.Comment: 21 pages, 18 figure

A mesoscopic model for the rheology of soft amorphous solids, with application to mi- crochannel flows

We study a mesoscopic model for the flow of amorphous solids. The model is based on the key features identified at the microscopic level, namely peri- ods of elastic deformation interspersed with localised rearrangements of parti- cles that induce long-range elastic deformation. These long-range deformations are derived following a continuum mechanics approach, in the presence of solid boundaries, and are included in full in the model. Indeed, they mediate spatial cooperativity in the flow, whereby a localised rearrangement may lead a distant region to yield. In particular, we simulate a channel flow and find manifestations of spatial cooperativity that are consistent with published experimental obser- vations for concentrated emulsions in microchannels. Two categories of effects are distinguished. On the one hand, the coupling of regions subject to different shear rates, for instance,leads to finite shear rate fluctuations in the seemingly un- sheared "plug" in the centre of the channel. On the other hand, there is convinc- ing experimental evidence of a specific rheology near rough walls. We discuss diverse possible physical origins for this effect, and we suggest that it may be associated with the bumps of particles into surface asperities as they slide along the wall

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear lattice defects is not applicable - still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.Comment: Journal of Statistical Mechanics: Theory and Experiment, 2015, P0201

Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity

A mesoscopic model for shear plasticity of amorphous materials in two dimensions is introduced, and studied through numerical simulations in order to elucidate the macroscopic (large scale) mechanical behavior. Plastic deformation is assumed to occur through a series of local reorganizations. Using a discretization of the mechanical fields on a discrete lattice, local reorganizations are modeled as local slip events. Local yield stresses are randomly distributed in space and invariant in time. Each plastic slip event induces a long-ranged elastic stress redistribution. Rate and thermal effects are not discussed in the present study. Extremal dynamics allows for recovering many of the complex features of amorphous plasticity observed experimentally and in numerical atomistic simulations in the quasi-static regime. In particular, a quantitative picture of localization, and of the anisotropic strain correlation both in the initial transient regime, and in the steady state are provided. In addition, the preparation of the amorphous sample is shown to have a crucial effect of on the localization behavior

Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity

A mesoscopic model for shear plasticity of amorphous materials in two dimensions is introduced, and studied through numerical simulations in order to elucidate the macroscopic (large scale) mechanical behavior. Plastic deformation is assumed to occur through a series of local reorganizations. Using a discretization of the mechanical fields on a discrete lattice, local reorganizations are modeled as local slip events. Local yield stresses are randomly distributed in space and invariant in time. Each plastic slip event induces a long-ranged elastic stress redistribution. Rate and thermal effects are not discussed in the present study. Extremal dynamics allows for recovering many of the complex features of amorphous plasticity observed experimentally and in numerical atomistic simulations in the quasi-static regime. In particular, a quantitative picture of localization, and of the anisotropic strain correlation both in the initial transient regime, and in the steady state are provided. In addition, the preparation of the amorphous sample is shown to have a crucial effect of on the localization behavior