Mapping between atomistic simulations and Eshelby inclusions in the shear deformation of an amorphous silicon model

Topological characterization of rearrangements in amorphous solids

In amorphous materials, plasticity is localized and occurs as shear transformations. It was recently shown by Wu et al. that these shear transformations can be predicted by applying topological defect concepts developed for liquid crystals to an analysis of vibrational eigenmodes [Z. W. Wu et al., Nat. Commun. 14, 2955 (2023)10.1038/s41467-023-38547-w]. This study relates the -1 topological defects to the displacement fields expected of an Eshelby inclusion, which are characterized by an orientation and the magnitude of the eigenstrain. A corresponding orientation and magnitude can be defined for each defect using the local displacement field around each defect. These parameters characterize the plastic stress relaxation associated with the local structural rearrangement and can be extracted using the fit to either the global displacement field or the local field. Both methods provide a reasonable estimation of the molecular-dynamics-measured stress drop, confirming the localized nature of the displacements that control both long-range deformation and stress relaxation.

Identifying microscopic factors that influence ductility in disordered solids

There are empirical strategies for tuning the degree of strain localization in disordered solids, but they are system-specific and no theoretical framework explains their effectiveness or limitations. Here, we study three model disordered solids: a simulated atomic glass, an experimental granular packing, and a simulated polymer glass. We tune each system using a different strategy to exhibit two different degrees of strain localization. In tandem, we construct structuro-elastoplastic (StEP) models, which reduce descriptions of the systems to a few microscopic features that control strain localization, using a machine learning-based descriptor, softness, to represent the stability of the disordered local structure. The models are based on calculated correlations of softness and rearrangements. Without additional parameters, the models exhibit semiquantitative agreement with observed stress-strain curves and softness statistics for all systems studied. Moreover, the StEP models reveal that initial structure, the near-field effect of rearrangements on local structure, and rearrangement size, respectively, are responsible for the changes in ductility observed in the three systems. Thus, StEP models provide microscopic understanding of how strain localization depends on the interplay of structure, plasticity, and elasticity.

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.

Residual stress in athermal soft disordered solids: insights from microscopic and mesoscale models

In soft amorphous materials, shear cessation after large shear deformation leads to configurations having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the shear cessation leads to lower residual stress states. We rationalise our findings using a mesoscopic elasto-plastic description that explicitly includes a long range elastic response to local shear transformations. We find that after flow cessation the initial stress relaxation indeed depends on the pre-sheared stress state, but the final residual stress is majorly determined by newly activated plastic events occurring during the relaxation process, a scenario consistent with the phenomenology of avalanche dynamics in the low shear rate limit of steadily sheared amorphous solids. Our simplified coarse grained description not only allows capturing the phenomenology of residual stress states but also rationalising the altered material properties that are probed using small and large deformation protocols applied to the relaxed material.

Predicting plasticity of amorphous solids from instantaneous normal modes

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the VDOS of affinely strained configurations at varying strain values. The affine strain, found analytically on the static (undeformed) snapshot of the glass, leads to configurations that are rich with soft low-energy modes as well as unstable modes (negative eigenvalues) that are otherwise completely "washed out" and lost if one lets the system fully relax after strain. This procedure is consistent with the structure of NALD. The INM spectrum of deformed states allows for the analytical prediction of the stress-strain curve of a model glass. Good parameter-free quantitative agreement is shown between the prediction and simulations of athermal quasistatic shear of a coarse-grained polymer glass.

Elastic criterion for shear-banding instability in amorphous solids

In amorphous solids, plastic flow is prone to localization into shear bands via an avalanche of shear-transformation (ST) rearrangements of constituent atoms or particles. However, such banding instability still remains a lack of direct experimental evidence. Using a real 3D colloidal glass under shear as proof of principle, we study STs' avalanches into shear banding that is controlled by strain rates. We demonstrate that, accompanying the emergent shear banding, the elastic response fields of the system, typical of a quadrupole for shear and a centrosymmetry for dilatation, lose the Eshelby-type spatial symmetry; instead, a strong correlation appears preferentially along the banding direction. By quantifying the fields' spatial decay, we identify an elastic criterion for the shear-banding instability, that is, the strongly correlated length of dilatation is smaller than the full length of shear correlation. Specifically, ST-induced free volume has to be confined within the elastic shear domain of ST so that those STs can self-organize to trigger shear banding. This physical picture is directly visualized by tracing the real-space evolution of local dilatation and ST particles. The present work unites the two classical mechanisms: free volume and STs, for the fundamental understanding of shear banding in amorphous solids.

Avalanche dynamics in sheared athermal particle packings occurs via localized bursts predicted by unstable linear response

Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter.

Low-energy quasilocalized excitations in structural glasses

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor F_α associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate F_α along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.

Origins of the change in mechanical strength of silicon/gold nanocomposites during irradiation

Silicon-based layered nanocomposites, comprised of covalent-metal interfaces, have demonstrated elevated resistance to radiation. The amorphization of the crystalline silicon sublayer during irradiation and/or heating can provide an additional mechanism for accommodating irradiation-induced defects. In this study, we investigated the mechanical strength of irradiated Si-based nanocomposites using atomistic modeling. We first examined dose effects on the defect evolution mechanisms near silicon-gold crystalline and amorphous interfaces. Our simulations reveal the growth of an emergent amorphous interfacial layer with increasing dose, a dominant factor mitigating radiation damage. We then examined the effect of radiation on the mechanical strength of silicon-gold multilayers by constructing yield surfaces. These results demonstrate a rapid onset strength loss with dose. Nearly identical behavior is observed in bulk gold, a phenomenon that can be rooted to the formation of radiation-induced stacking fault tetrahedra which dominate the dislocation emission mechanism during mechanical loading. Taken together, these results advance our understanding of the interaction between radiation-induced point defects and metal-covalent interfaces.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

An Insight into Amorphous Shear Band in Magnetorheological Solid by Atomic Force Microscope

Micro mechanism consideration is critical for gaining a thorough understanding of amorphous shear band behavior in magnetorheological (MR) solids, particularly those with viscoelastic matrices. Heretofore, the characteristics of shear bands in terms of formation, physical evolution, and response to stress distribution at the localized region have gone largely unnoticed and unexplored. Notwithstanding these limitations, atomic force microscopy (AFM) has been used to explore the nature of shear band deformation in MR materials during stress relaxation. Stress relaxation at a constant low strain of 0.01% and an oscillatory shear of defined test duration played a major role in the creation of the shear band. In this analysis, the localized area of the study defined shear bands as varying in size and dominantly deformed in the matrix with no evidence of inhibition by embedded carbonyl iron particles (CIPs). The association between the shear band and the adjacent zone was further studied using in-phase imaging of AFM tapping mode and demonstrated the presence of localized affected zone around the shear band. Taken together, the results provide important insights into the proposed shear band deformation zone (SBDZ). This study sheds a contemporary light on the contentious issue of amorphous shear band deformation behavior and makes several contributions to the current literature.

Elastoplastic Approach Based on Microscopic Insights for the Steady State and Transient Dynamics of Sheared Disordered Solids

We develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse-grained quantities from simulations of dense disordered particulate systems, we present a coherent elastoplastic model approach for deformation and flow of yield stress materials. For a given set of parameters, this model allows us to match consistently transient and steady state features of driven disordered systems with diverse preparation histories under both applied shear-rate and creep protocols.

Time-resolved shear transformations in the transient plastic regime of sheared amorphous silicon

The accumulation of shear transformations (STs) in space and time is responsible for plastic deformation in amorphous solids. Here we study the effect of finite strain rates on STs during simulations of athermal shear deformation in an atomistic model of amorphous silicon. We present a time-resolved analysis of STs by mapping the plastic events identified in the atomistic simulations on a collection of Eshelby inclusions, which are characterized in terms of number, effective volume, lifetime, and orientation. Our analysis led us to distinguish between small and large events. We find that the main effect of a lower strain rate is to allow for a larger number of small events, roughly identified by an effective volume γ_{0}V_{0}<20 Å^{3}, while the number and characteristics of larger events are surprisingly independent of the strain rate. We show that at low strains, the decrease of the stress observed at lower strain rates is mainly due to the excess of small events, while at larger strains, when the glass approaches the yield point where a shear band forms, larger events start to play a role and organize due to their elastic interactions. This phenomenology is compared with the predictions of mesoscale elastoplastic models. The technique developed here can be used as a systematic tool to analyze plasticity during molecular dynamics simulations. It can also give valuable information to develop physically grounded mesoscale models of plasticity, providing quantitative predictions of the mechanical properties of amorphous materials.

Residual stress distributions in amorphous solids from atomistic simulations

The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress differences between plastic events. Results further suggest that the local yield stress in amorphous solids changes even if the given region does not participate in plastic activity.

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals, and boundary effects

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e., they feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that, in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce the fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both two and three dimensions. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.

Origin of reversible and irreversible atomic-scale rearrangements in a model two-dimensional network glass

In this contribution, we investigate the fundamental mechanism of plasticity in a model two-dimensional network glass. The glass is generated by using a Monte Carlo bond-switching algorithm and subjected to athermal simple shear deformation, followed by subsequent unloading at selected deformation states. This enables us to investigate the topological origin of reversible and irreversible atomic-scale rearrangements. It is shown that some events that are triggered during loading recover during unloading, while some do not. Thus, two kinds of elementary plastic events are observed, which can be linked to the network topology of the model glass.

Continuum constitutive laws to describe acoustic attenuation in glasses

Nowadays metamaterials are at the focus of an intense research as promising for thermal and acoustic engineering. However, the computational cost associated to the large system size required for correctly simulating them imposes the use of finite-elements simulations, developing continuum models, able to grasp the physics at play without entering in the atomistic details. Still, a correct description should be able to reproduce not only the extrinsic scattering sources on waves propagation, as introduced by the metamaterial microstructure, but also the intrinsic wave attenuation of the material itself. This becomes dramatically important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scale in amorphous materials and describe phonon attenuation due to atomistic mechanisms, characterized by a defined frequency dependence. This represents a first decisive step for investigating the effect of a complex nano- or microstructure on acoustic attenuation, while including the atomistic contribution as well.

Connecting shear localization with the long-range correlated polarized stress fields in granular materials

One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a deep connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular material subject to shear. Specifically, we find strong (anti)correlations between the micro shear bands and two polarized stress fields along two directions of maximal shear. By exploring the tensorial characteristics and the rotational symmetry of force network, we reveal that such profound connection is a result of symmetry breaking by shear. Finally, we provide the solid experimental evidence of long-range correlated inherent shear stress in an isotropically jammed granular system.

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.

Propagative and diffusive regimes of acoustic damping in bulk amorphous material

In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the dynamical dtructure factor (DSF) thanks to inelastic neutron or x-ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave-packet propagation in numerical models of amorphous silicon. We show that the damped harmonic oscillator model fits of the dynamical structure factors give a good estimate of the wave packets mean free path, only below the Ioffe-Regel frequency. Above the Ioffe-Regel frequency and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel frequency, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in detail and reveals a complex dynamics for energy transport, thus raising the question of the correct modeling of thermal transport in amorphous materials.

Critical exponents of the yielding transition of amorphous solids

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ[over ̇]∼(σ-σ_{c})^{β}. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.

Cellulose crystals plastify by localized shear

While most attention has so far been devoted to the tensile properties of crystalline cellulose, the main elementary building block of plants, we show here using atomistic simulations that their shear is also an important mode of deformation, occurring at stress levels lower than tension with much larger ductility. We also demonstrate how crystalline defects like dislocations drastically facilitate plasticity. This analysis can be used as a basis for the micromechanical modeling of cellulose microfibrils that are currently considered as promising eco-friendly alternatives to synthetic fibers for structural materials.

Cellulose microfibrils are the principal structural building blocks of wood and plants. Their crystalline domains provide outstanding mechanical properties. Cellulose microfibrils have thus a remarkable potential as eco-friendly fibrous reinforcements for structural engineered materials. However, the elastoplastic properties of cellulose crystals remain poorly understood. Here, we use atomistic simulations to determine the plastic shear resistance of cellulose crystals and analyze the underpinning atomic deformation mechanisms. In particular, we demonstrate how the complex and adaptable atomic structure of crystalline cellulose controls its anisotropic elastoplastic behavior. For perfect crystals, we show that shear occurs through localized bands along with noticeable dilatancy. Depending on the shear direction, not only noncovalent interactions between cellulose chains but also local deformations, translations, and rotations of the cellulose macromolecules contribute to the response of the crystal. We also reveal the marked effect of crystalline defects like dislocations, which decrease both the yield strength and the dilatancy, in a way analogous to that of metallic crystals.

Orientation of plastic rearrangements in two-dimensional model glasses under shear

The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20^{∘}. The distributions of sizes and orientations of shear transformations display no substantial sensitivity to the shear rate. These results can notably be used to refine the description of rearrangements in elastoplastic models.

Local yield stress statistics in model amorphous solids

We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.

Mean-Field Scenario for the Athermal Creep Dynamics of Yield-Stress Fluids

We develop a theoretical description based on an existent mean-field model for the transient dynamics prior to the steady flow of yielding materials. The mean-field model not only reproduces the experimentally observed nonlinear time dependence of the shear-rate response to an external stress, but also allows for the determination of the different physical processes involved in the onset of the reacceleration phase after the initial slowing down and a distinct fluidization phase. The fluidization time displays a power-law dependence on the distance of the applied stress to an age-dependent yield stress, which is not universal but strongly dependent on initial conditions.

Non-trivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins of 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.

Universal features of amorphous plasticity

Plastic yielding of amorphous solids occurs by power-law distributed deformation avalanches whose universality is still debated. Experiments and molecular dynamics simulations are hampered by limited statistical samples, and although existing stochastic models give precise exponents, they require strong assumptions about fixed deformation directions, at odds with the statistical isotropy of amorphous materials. Here, we introduce a fully tensorial, stochastic mesoscale model for amorphous plasticity that links the statistical physics of plastic yielding to engineering mechanics. It captures the complex shear patterning observed for a wide variety of deformation modes, as well as the avalanche dynamics of plastic flow. Avalanches are described by universal size exponents and scaling functions, avalanche shapes, and local stability distributions, independent of system dimensionality, boundary and loading conditions, and stress state. Our predictions consistently differ from those of mean-field depinning models, providing evidence that plastic yielding is a distinct type of critical phenomenon.

The universality class for plastic yield in amorphous materials remains controversial. Here authors present a tensorial mesoscale model that captures both complex shear patterns and avalanche scaling behaviour, which differs from mean-field models and suggests a distinct type of critical phenomenon.

Effect of composition and pressure on the shear strength of sodium silicate glasses: An atomic scale simulation study

The elastoplastic behavior of sodium silicate glasses is studied at different scales as a function of composition and pressure, with the help of quasistatic atomistic simulations. The samples are first compressed and then sheared at constant pressure to calculate yield strength and permanent plastic deformations. Changes occurring in the global response are then compared to the analysis of local plastic rearrangements and strain heterogeneities. It is shown that the plastic response results from the succession of well-identified localized irreversible deformations occurring in a nanometer-size area. The size and the number of these local rearrangements, as well as the amount of internal deviatoric and volumetric plastic deformation, are sensitive to the composition and to the pressure. In the early stages of the deformation, plastic rearrangements are driven by sodium mobility. Consequently, the elastic yield strength decreases when the sodium content increases, and the same when pressure increases. Finally, good correlation was found between global and local stress-strain relationships, reinforcing again the role of sodium ions as local initiators of the plastic behavior observed at larger scales.

Shear transformation distribution and activation in glasses at the atomic scale

We characterize shear transformations (STs) at the atomic scale in a model of amorphous silicon using a mapping on Eshelby inclusions. We investigate the effect of pressure, glass relaxation, as well as damage on the ST characteristics. We show that the characteristic ST effective volume, γ_{0}V_{0}, product of the ST plastic shear strain γ_{0} and volume V_{0}, does not depend significantly on an applied pressure but increases with accumulated plastic deformation from about 10Å^{3} in the pseudoelastic regime to about 60Å^{3} once plastic flow sets in. Furthermore, by using nudged elastic band calculations, we measure the energy barrier against ST activation. Analyzing different paths leading to either an isolated ST or an avalanche, we show that the barrier is systematically controlled by the first ST with an activation volume equal to the effective volume of the ST at the activated state, which represents only a fraction of the complete ST volume. The activation volume is also found smaller for avalanches, presumably because of accumulated local damage. This work provides essential information to build reliable mesoscale models of plasticity.