Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent years. Investigations employing both unidirectional and cyclic deformation protocols reveal a strong dependence of yielding behaviour on the degree of annealing. Below a threshold degree of annealing, the nature of yielding changes qualitatively, to progressively more discontinuous yielding. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on yielding under unidirectional deformation, but cyclic deformation reveals several interesting features that remain largely un-investigated. Focusing on athermal cyclic deformation, I investigate a family of models based on an energy landscape description. These models reproduce key interesting features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous sh…
A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be co…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The intrinsic dissolution rate is shown to be proportional to the concentration of surface particles kinetically able to exchange with the solvent, independent of temperature or the thermal history of the glass. The morphology of the dissolving surface is described and the possibility of using surface etching to image dynamic heterogeneities is explored.
The non-equilibrium dynamics of an amorphous solid is studied with a soft-spin type model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts (KWW) form similar to that obtained in Phys. Rev. Lett. {\bf 95}, 055702 (2005) from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem (FDT) violation is also studied in the time as well as correlation windows.
The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several different approaches to explain the thermal conductivities for these systems, for example, the Bridgman's formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to explain the thermal conductivities of liquids and amorphous solids in a unified way. The calculated thermal conductivities using this form…
Amorphous magnetic solids, like metallic glasses, exhibit a novel effect: the growth of magnetic order as a function of mechanical strain under athermal conditions in the presence of a magnetic field. The magnetic moment increases in steps whenever there is a plastic event. Thus plasticity induces the magnetic ordering, acting as the effective noise driving the system towards equilibrium. We present results of atomistic simulations of this effect in a model of a magnetic amorphous solid subjected to pure shear and a magnetic field. To elucidate the dependence on external strain and magnetic fi…
Standard approaches to magneto-mechanical interactions in thermal magnetic crystalline solids involve Landau functionals in which the lattice anisotropy and the resulting magnetization easy axes are taken explicitly into account. In glassy systems one needs to develop a theory in which the amorphous structure precludes the existence of an easy axis, and in which the constituent particles are free to respond to their local amorphous surroundings and the resulting forces. We present a theory of all the mixed responses of an amorphous solids to mechanical strains and magnetic fields. Atomistic mo…
The yield of amorphous solids like metallic glasses under external stress was discussed asserting that it is related to the glass transition by increasing temperature, or that it can be understood using statistical theories of various sorts. Here we study the approach to stress-controlled yield and argue that neither assertions can be supported, at least at low temperatures. The yield of amorphous solids at low temperatures is a highly structured phenomenon, characterized by a specific series of mechanical instabilities, and having no similarity at all to fluidization by increased temperature,…
Amorphous solids yield at a critical value $Σ_c$ of the imposed stress $Σ$ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below $Σ_c$. Here, we study the steady state thermal flow of amorphous solids using a mesoscopic elasto-plastic model. In the Hebraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that …
The fundamental instability responsible for the shear localization which results in shear bands in amorphous solids remains unknown despite enormous amount of research, both experimental and theoretical. As this is the main mechanism for the failure of metallic glasses, understanding the instability is invaluable in finding how to stabilize such materials against the tendency to shear localize. In this Letter we explain the mechanism for shear localization under shear, which is the appearance of highly correlated lines of Eshelby-like quadrupolar singularities which organize the non-affine pla…
We build a mean-field model of plasticity of amorphous solids, based on the dynamics of an ensemble shear transformation zones, interacting via intrinsic dynamical noise generated by the zone flips themselves. We compare the quasi-static, steady-state properties for two types of noise spectrum: (G) Gaussian; (E) broad distribution derived from quadrupolar elastic interactions. We find that the plastic flow proceeds via avalanches whose scaling properties with system size are highly sensitive to noise tails. Comparison with available data suggests that non-affine strain fields might be of param…
When submitted to a constant mechanical load, many amorphous solids display power law creep followed by fluidization. A fundamental understanding of these processes is still far from being achieved. Here, we characterize creep and fluidization on the basis of a mesoscopic viscoplastic model that includes thermally activated yielding events and a broad distribution of energy barriers, which may be lowered under the effect of a local deformation. We relate the creep exponent observed before fluidization to the width of barrier distribution and to the specific form of stress redistribution follow…
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses, emulsions and granular packings -- are useful as structural materials in a variety of contexts. Their deformation and flow behaviour is relevant for many others. Apart from fundamental questions associated with the formation of these solids, comprehending their mechanical behaviour is thus of interest, and of significance for their use as materials. In parti…
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim (z - 2d)^{-1/2}$, where $z \ge 2d$ is the mean coordination, and $d$ is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale $\ell_c$ is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of $\ell_c\sim (p_c-p)^{-1/4}$ with proximity to a critical internal s…
Plastic events in amorphous solids can be much more than just "shear transformation zones" when the positional degrees of freedom are coupled non-trivially to other degrees of freedom. Here we consider magnetic amorphous solids where mechanical and magnetic degrees of freedom interact, leading to rather complex plastic events whose nature must be disentangled. In this paper we uncover the anatomy of the various contributions to some typical plastic events. These plastic events are seen as Barkhausen Noise or other "serrated noises". Using theoretical considerations we explain the observed stat…
The mechanical response of solids depends on temperature because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in metallurgy, aerospace engineering, energy. In glasses the vanishing of rigidity upon increasing temperature is the reverse process of the glass transition. It remains poorly understood due to the disorder leading to nontrivial (nonaffine) components in the atomic displacements. Our theory explains the basic mechanism of the melting transit…
Using numerical simulations, we study the failure of an amorphous solid under quasi-static expansion starting from a homogeneous high-density state. During the volume expansion, we demonstrate the existence of instabilities manifesting via saddle-node bifurcation in which a minimum meets a saddle. During all such events, the smallest eigenvalue of the Hessian matrix vanishes as a square-root singularity. The plastic instabilities are manifested via sudden jumps in pressure and energy, with the largest event happening when a cavity appears, leading to the yielding of the material. We show that …
Yield stress materials fail when the imposed stress crosses a critical threshold. A well-known dynamical response to the applied stress is the phenomenon of creep where the cumulative deformation grows sublinearly with time, prior to failure or arrest. Using extensive molecular dynamics simulations, we study such response for a model amorphous system, in the athermal limit, and probe how the annealing history of the initial state determines the observed behaviour to an applied shear stress. Further, we analyze the microscopic dynamics in the vicinity of the yield threshold, using large systems…
We report on a particle-based numerical study of sheared amorphous solids in the dense slow flow regime. In this framework, deformation and flow are accompanied by critical fluctuation patterns associated with the macroscopic plastic response and single particle kinematics. The former is commonly attributed to the collective slip patterns that relax internal stresses within the bulk material and give rise to an effective mechanical noise governing the latter particle-level process. In this work, the avalanche-type dynamics between plastic events is shown to have a strong relevance on the self-…
We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and meso-scale elasto-plastic models (EPM) for amorphous solids sheared in the athermal quasi-static limit. We show that the spatial correlations in plastic activity exhibit a short lengthscale that grows as $t^{3/4}$ in MD and ballistically in EPM, and is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similari…
The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's stability. Here we study the stability dependence of the local elastic constants of a simulated glass former over a broad range of stabilities, from a poorly annealed glass to a glass whose stability is comparable to laboratory exceptionally stable vapor deposited glasses. We show that with increasing stability the glass becomes more uniform as evidenced by a s…
The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three disks. The maximum contact number per particle pair is defined and proposed as a useful means of categorizing particle shape. We demonstrate that the densest packed crystal exhibits a maximum in the number of contacts per particle but does not necessarily include particle pairs with the maximum contact number. In contrast, amorphous structures, generated by energy minimization of high temperature liquids, typically do include maximum contact pairs. The am…
We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a thr…
Fast scanning calorimetry (FSC) was employed to investigate glass softening dynamics in amorphous solid water (ASW) nano-aggregates with thicknesses ranging from 2 to 20 nm. ASW nano-aggregates were prepared by vapor-deposition on the surface of a tungsten filament near 141 K and then heated at a rate of 100 kK/s. The resulting thermogram complex endo- and exothermal features were analyzed using a simple model. The results of the analysis show that glass softening of ASW nano-aggregates takes place at 160 K and vaporization of ASW nano-aggregates can take place at temperatures as low as 185 K.…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a…
The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers. In this study, we present results of {\em in silico} mechanical deformation experiments from two very different model solids in two and three dimensions. The first consists of particles interacting with isotropic potentials and the other has strongly direction dependent interactions. We show that in both cases, the excess vibrational density of states is the fundamental quantity which …
The yielding transition of amorphous materials is studied with a two-dimensional Hamiltonian model that allows both shear and volume deformations. The model is investigated as a function of the relative value of the bulk modulus $B$ with respect to the shear modulus $μ$. When the ratio $B/μ$ is small enough, the yielding transition becomes discontinuous, yet reversible. If the system is driven at constant strain rate in the coexistence region, a spatially localized shear band is observed while the rest of the system remains blocked. The crucial role of volume fluctuations in the origin of this…
Yielding transitions in athermal amorphous materials resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, …
We study the shear induced fluidization of amorphous solids subjected to external loading by investigating the relaxation dynamics of the deformed states using computer simulation. A simple shear deformation is employed at constant rate to the thermal glassy materials. The shear localization and the plastic deformation heterogeneity with strain is investigated in terms of the non-affine displacement field. The mean square displacement shows an enhanced mobility of the particles with strain, indicating the fluidization of the material. Using the time correlation function we estimate the relaxat…
We study the rheology of amorphous solids in the limit of negligible thermal fluctuations. On the basis of general arguments, the flow curve is shown to result from an interplay between the time scales of the macroscopic driving and the (cascades of) local particle rearrangements. Such rearrangements are known to induce a redistribution of the elastic stress in the system. Although mechanical noise, i.e., the local stress fluctuations arising from this redistribution, is widely believed to activate new particle rearrangements, we provide evidence that casts severe doubt on the analogy with the…
Amorphous solids yield in strain-controlled protocols at a critical value of the strain. For larger strains the stress and energy display a generic complex serrated signal with elastic segments punctuated by sharp energy and stress plastic drops having a wide range of magnitudes. Here we provide a theory of the scaling properties of such serrated signals taking into account the system-size dependence. We show that the statistics are not homogeneous - they separate sharply to a regime of `small' and `large' drops, each endowed with its own scaling properties. A scaling theory is first derived s…
Using numerical simulations, we have studied the yielding response, in the athermal quasi static limit, of a model amorphous material having inclusions in the form of randomly pinned particles. We show that, with increasing pinning concentration, the plastic activity becomes more spatially localized, resulting in smaller stress drops, and corresponding increase in the magnitude of strain where yielding occurs. We demonstrate that, unlike the spatially heterogeneous and avalanche led yielding in the case of the unpinned glass, for the case of large pinning concentration, yielding takes place vi…
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress vs. strain curves, and pro…
Highly acurate numerical simulations are employed to highlight the subtle but important differences in the mechanical stability of perfect crystalline solids versus amorphous solids. We stress the difference between strain values at which the shear modulus vanishes and strain values at which a plastic instability insues. The temperature dependence of the yield strain is computed for the two types of solids, showing different scaling laws: $γ_{_{Y}}\simeq γ_{_{Y}}^{0}-C_1 T^{1/3}$ for crystals versus $γ_{_{Y}}\simeq γ_{_{Y}}^{0}- C_2 T^{2/3}$ for amorphous solids.
We address the cross effects between mechanical strains and magnetic fields on the plastic response of magnetoelastic amorphous solids. It is well known that plasticity in non-magnetic amorphous solids under external strain $γ$ is dominated by the co-dimension 1 saddle-node bifurcation in which an eigenvalue of the Hessian matrix vanishes at $γ_P$ like $\sqrt{γ_P-γ}$. This square-root singularity determines much of the statistical physics of elasto-plasticity, and in particular that of the stress-strain curves under athermal-quasistatic conditions. In this Letter we discuss the much richer phy…
We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more re…
We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite size effects in brittle yielding a…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The Hessian matrix, associated with infinitesimal fluctuations around the stationary point corresponding to the amorphous solid state, is obtained. The eigenvalues of this Hessian matrix are all shown to be strictly positive near the transition, except for one--the zero mode associated with the spontaneously broken continuous translational symmetry of the system. Th…
Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively[1-14], observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transiti…
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 {\em differences} between plastic events. Results f…
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 th…
We propose a method to predict the value of the external strain where a generic amorphous solid will fail by a plastic response (i.e. an irreversible deformation), solely on the basis of measurements of the nonlinear elastic moduli. While usually considered fundamentally different, with the elastic properties describing reversible phenomena and plastic failure epitomizing irreversible behavior, we show that the knowledge of some nonlinear elastic moduli is enough to predict where plasticity sets in.
We present results of atomistic simulations of a new model of a magnetic amorphous solid subjected to external mechanical strains and magnetic fields. The model employed offers new perspectives on important effects like Barkhausen noise and magnetostriction. It is shown that the plastic response in such systems exhibit singularities characterized by unexpected exponents requiring careful theoretical reasoning. The spatial structure of the plastic events requires a new coarse grained elasto-magnetic theory which is provided here.
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the one of disordered magnetic materials. Here we show that in…
A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a 2D athermal amorphous solid with oscillatory shear, and show that a suitable readout protocol reveals the shearing amplitude. When shearing alternates between two amplitudes, signatures of both values are retained only if the smaller one is applied last. We show that these behaviors arise because individual clusters of rearrangements are hysteretic and dissipative, and because different clusters respond differently to…
It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous (LDA) ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second "distinct" high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations, and find that VHDA is a more stable form of HDA and that in fact VHDA should be c…
We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. While the amorphous solids are long-lived and slowly-aging glasses, …
Goldstone modes in the amorphous solid state, resulting from the spontaneous breaking of translational symmetry due to random localisation of particles, are discussed. Starting from a microscopic model with quenched disorder, the broken symmetry is identified to be that of relative translations of the replicas. Goldstone excitations, corresponding to pure shear deformations, are constructed from long wavelength distortions of the order parameter. The elastic free energy is computed, and it is shown that Goldstone fluctuations destroy localisation in two spatial dimensions, yielding a two-dimen…
``Shear softening" refers to the observed reduction in shear modulus when the stress on an amorphous solid is increased beyond the initial linear region. Careful numerical quasi-static simulations reveal an intimate relation between plastic failure and shear softening. The attaintment of the steady-state value of the shear modulus associated with plastic flow is identified with a percolation of the regions that underwent a plastic event. We present an elementary ``two-state" model that interpolates between failed and virgin regions and provides a simple and effective characterization of the sh…
