Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

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.

Plasticity in Amorphous Solids Is Mediated by Topological Defects in the Displacement Field

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatiotemporal correlations in the undeformed glass that may trigger plastic instability. In contrast, in this Letter we show that the topological defects that correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) that are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular nonlocal peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between antiparallel DTDs; and (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45° for uniaxial deformations, as widely observed in experiments and simulations.

Yielding in an amorphous solid subject to constant stress at finite temperatures

Understanding the nature of the yield transition is a long-standing problem in the physics of amorphous solids. Here we use molecular dynamics simulations to study the response of amorphous solids to constant stresses at finite temperatures. We compare amorphous solids that are prepared using fast and slow quenches and show that for thermal systems, the steady-state velocity exhibits a continuous transition from very slow creep to a finite strain rate as a function of the stress. This behavior is observed for both well-annealed and poorly annealed systems. However, the transient dynamics is different in the latter and involves overcoming an energy barrier. Due to the different simulation protocol, the strain rate as a function of stress and temperature follows a scaling relation that is different from the ones that are shown for systems where the strain is controlled. Collapsing the data using this scaling relation allows us to calculate critical exponents for the dynamics close to yield, including an exponent for thermal rounding. We also demonstrate that strain slips due to avalanche events above yield follow standard scaling relations and we extract critical exponents that are comparable to the ones obtained in previous studies that performed simulations of both molecular dynamics and elastoplastic models using strain-rate control.

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.

Renormalization of elastic quadrupoles in amorphous solids

Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the model problem of an elastic continuum with quadrupolar defects, at finite temperature. This problem is posed and the collective behavior of the defects is analytically investigated. Using both renormalization group and field-theoretic techniques, it is found that the model has a yielding/melting transition of spinodal type.

Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates

We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) ∼S^-τ_Sf(S/L^d_f) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃P(0) + x^θ with P(0) ∼L^-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent β ([small gamma, Greek, dot above]∼ (σ-σ_c)^β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Random critical point separates brittle and ductile yielding transitions in amorphous materials

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.