Yielding of glass under shear: A directed percolation transition precedes shear-band formation

Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.

Brittle and ductile yielding in soft materials

Many soft materials yield under mechanical loading, but how this transition from solid-like behavior to liquid-like behavior occurs can vary significantly. Understanding the physics of yielding is of great interest for the behavior of biological, environmental, and industrial materials, including those used as inks in additive manufacturing and muds and soils. For some materials, the yielding transition is gradual, while others yield abruptly. We refer to these behaviors as being ductile and brittle. The key rheological signatures of brittle yielding include a stress overshoot in steady-shear-startup tests and a steep increase in the loss modulus during oscillatory amplitude sweeps. In this work, we show how this spectrum of yielding behaviors may be accounted for in a continuum model for yield stress materials by introducing a parameter we call the brittility factor. Physically, an increased brittility decreases the contribution of recoverable deformation to plastic deformation, which impacts the rate at which yielding occurs. The model predictions are successfully compared to results of different rheological protocols from a number of real yield stress fluids with different microstructures, indicating the general applicability of the phenomenon of brittility. Our study shows that the brittility of soft materials plays a critical role in determining the rate of the yielding transition and provides a simple tool for understanding its effects under various loading conditions.

Criticality in the fracture of silica glass: Insights from molecular mechanics

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

Direct Observation of Quadrupolar Strain Fields forming a Shear Band in Metallic Glasses

For decades, scanning/transmission electron microscopy (S/TEM) techniques have been employed to analyze shear bands in metallic glasses and understand their formation in order to improve the mechanical properties of metallic glasses. However, due to a lack of direct information in reciprocal space, conventional S/TEM cannot characterize the local strain and atomic structure of amorphous materials, which are key to describe the deformation of glasses. For this work, 4-dimensional-STEM (4D-STEM) is applied to map and directly correlate the local strain and the atomic structure at the nanometer scale in deformed metallic glasses. Residual strain fields are observed with quadrupolar symmetry concentrated at dilated Eshelby inclusions. The strain fields percolate in a vortex-like manner building up the shear band. This provides a new understanding of the formation of shear bands in metallic glass.

Upper bound of fragility from spatial fluctuations of shear modulus and boson peak in glasses

It is shown that the normalized rms fluctuation of the shear modulus on the medium-range order scale in glasses correlates with fragility: the higher fragility, the smaller the fluctuation amplitude. The latter is calculated within the heterogeneous elasticity theory using the data on the boson peak in glasses. On a smaller scale corresponding to cooperative structural relaxation, the normalized rms fluctuation of the infinite-frequency shear modulus was estimated using the data on the decoupling of viscosity and diffusion in supercooled liquids. These fluctuations are much smaller in amplitude, and, in contrast, they increase with increasing fragility. Extrapolation predicts intersection of both rms fluctuations and disappearing of the boson peak at the upper limit to fragility ≈180.

Annealing glasses by cyclic shear deformation

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory

Molecular dynamics computer simulations of a polydisperse soft-sphere model under shear are presented. The starting point for these simulations are deeply supercooled samples far below the critical temperature, T c, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below T c, we identify a lifetime τlt that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of τlt can be well described by an Arrhenius law. The existence of transient amorphous solid states below T c is associated with the possibility of brittle yielding, as manifested by a sharp stress drop in the stress–strain relation and shear banding. We show that brittle yielding requires, on the one hand, low shear rates and, on the other hand, the time scale corresponding to the inverse shear rate has to be smaller or of the order of τlt. Both conditions can only be met for a large lifetime τlt, i.e., for states far below T c.

Anisotropic correlations of plasticity on the yielding of metallic glasses

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

The initiation of shear band formation in deformed metallic glasses from soft localized domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u²⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u²⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

Mechanical properties and pore size distribution in athermal porous glasses

We study the mechanical properties and pore structure in a three-dimensional molecular dynamics model of porous glass under athermal quasistatic shear. The vitreous samples are prepared by rapid thermal quenching from a high-temperature molten state. The pore structures form via solid-gas phase separation. The quiescent samples exhibit a wide range of pore topography, from inter-connected pore networks to randomly distributed compact pores depending on the material density. We find that the shear modulus strongly depends on the density and porosity. Under mechanical loading, the pore structure rearranges which is reflected in the pore size distribution function. Our results show that with increase in strain the distribution widens as the adjacent pores coalesce and form larger pores. We also propose a universal scaling law for the pore size distribution function which offers excellent data collapse for highly porous materials in the undeformed case. From the data scaling, we identify a critical density that can be attributed to the transition point from a porous-type to bulk-type material. The validity of the scaling law under finite deformation is also analyzed.

On the yielding of a point-defect-rich model crystal under shear: insights from molecular dynamics simulations

In real crystals and at finite temperatures point defects are inevitable. Under shear their dynamics severely influence the mechanical properties of these crystals, giving rise to non-linear effects, such as ductility. In an effort to elucidate the complex behavior of crystals under plastic deformation it is crucial to explore and to understand the interplay between the timescale related to the equilibrium point-defect diffusion and the shear-induced timescale. Based on extensive non-equilibrium molecular dynamics simulations we present a detailed investigation on the yielding behavior of cluster crystals, an archetypical model for a defect-rich crystal: in such a system clusters of overlapping particles occupy the lattice sites of a regular (FCC) structure. In equilibrium particles diffuse via site-to-site hopping while maintaining the crystalline structure intact. We investigate these cluster crystals at a fixed density and at different temperatures where the system remains in the FCC structure: temperature allows us to vary the diffusion timescale appropriately. We then expose the crystal to shear, thereby choosing shear rates which cover timescales that are both higher and lower than the equilibrium diffusion timescales. We investigate the macroscopic and microscopic response of our cluster crystal to shear and find that the yielding scenario of such a system does not rely on the diffusion of the particles - it is rather related to the plastic deformation of the underlying crystalline structure. The local bond order parameters and the measurement of local angles between neighboring clusters confirm the cooperative movement of the clusters close to the yield point. Performing complementary, related simulations for an FCC crystal formed by harshly repulsive particles reveals similarities in the yielding behavior between both systems. Still we find that the diffusion of particles does influence characteristic features in the cluster crystal, such as a less prominent increase of order parameters close to the yield point. Our simulations provide for the first time an insight into the role of the diffusion of defects in the yielding behavior of a defect-rich crystal under shear. These observations will thus be helpful in the development of theories for the plastic deformation of defect-rich crystals.

Universality of plastic instability and mechanical yield in metallic glasses

The generic response of a wide range of amorphous solids is the average increase of stress upon external loading until the yielding transition point, after which elasto-plastic steady state sets in. The stress-strain response comprises of a series of elastic branches interspersed with plastic drops. The ubiquitousness of these phenomena indicates universality, independent of material property, but the literature predominantly deals with specific materials. In pursuit of generality among different amorphous systems, we undertake a careful investigation in the mechanical response of metallic glasses using computer simulation. By comparing our results of multi-body metallic glass potentials to those obtained from pairwise Lennard-Jones glasses, we show that the mechanism of plastic instabilities is universal and independent of the details of the underlying potential. We also investigate the yielding transition in terms of the overlap parameterQ₁₂, which has been successfully used Lennard-Jones glasses. The yielding is unambiguously identified as a first-order phase transition. These observations conform the nature of plastic instabilities and mechanical yield as universal and independent of microscopic interactions.

An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n c = 3.67 × 10-3 Å-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n g = 8.40 × 10-3 Å-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n c, subdiffusive for n c ≤ n < n g, and blocked for n ≥ n g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.

Dynamical modes of sheared confined microscale matter

Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velocities per ring. The first one is characterized by rare slip events, where the inner rings momentarily depin from the outer ring, which is kept static by the set of optical traps. For the second state, we find a bistability of the mean angular velocities, which can be understood from the analysis of the slip events in the particle trajectories. We calculate the particle waiting- and jumping time distributions and estimate a time scale between slips, which is also reflected by a plateau in the mean squared azimuthal displacement. The dynamical transition is further reflected by the components of the stress tensor, revealing a shear-thinning behavior as well as shear stress overshoots. Finally, we briefly discuss the observed transition in the context of stochastic thermodynamics and how it may open future directions in this field.

Ductile and Brittle Yielding in Thermal and Athermal Amorphous Materials

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 shear, which causes a shear banding instability that becomes more severe with increasing annealing. Ductile and brittle yielding thereby emerge as two limiting cases of a continuum of yielding transitions, from gradual to catastrophic. In contrast, athermal systems with a stress overshoot always show brittle yielding at low shear rates, however small the overshoot.

Flow heterogeneities in supercooled liquids and glasses under shear

Using extensive nonequilibrium molecular dynamics simulations, we investigate a glass-forming binary Lennard-Jones mixture under shear. Both supercooled liquids and glasses are considered. Our focus is on the characterization of inhomogeneous flow patterns such as shear bands that appear as a transient response to the external shear. For the supercooled liquids, we analyze the crossover from Newtonian to non-Newtonian behavior with increasing shear rate γ[over ̇]. Above a critical shear rate γ[over ̇]_{c} where a non-Newtonian response sets in, the transient dynamics are associated with the occurrence of short-lived vertical shear bands, i.e., bands of high mobility that form perpendicular to the flow direction. In the glass states, long-lived horizontal shear bands, i.e., bands of high mobility parallel to the flow direction, are observed in addition to vertical ones. The systems with shear bands are characterized in terms of mobility maps, stress-strain relations, mean-squared displacements, and (local) potential energies. The initial formation of a horizontal shear band provides an efficient stress release, corresponds to a local minimum of the potential energy, and is followed by a slow broadening of the band towards the homogeneously flowing fluid in the steady state. Whether a horizontal or a vertical shear band forms cannot be predicted from the initial undeformed sample. Furthermore, we show that with increasing system size, the probability for the occurrence of horizontal shear bands increases.

Length-scales of dynamic heterogeneity in a driven binary colloid

Here we study the characteristic length scales in an aqueous suspension of a symmetric oppositely charged colloid subjected to a uniform electric field by Brownian dynamics simulations. We consider the in-plane structure in the presence of a sufficiently strong electric field where the like charges in the system form macroscopic lanes. We construct spatial correlation functions characterizing the structural order and that of particles of different mobilities in the plane transverse to the electric field at a given time. We call these functions equal time density correlation functions (ETDCFs). The ETDCFs between particles of different charges, irrespective of mobilities, are the structural ETDCFs, while those between particles of different mobilities are the dynamic ETDCFs. We extract the characteristic length of correlation by fitting the envelopes of the ETDCFs to exponential dependences. We find that the correlation length scales of the structural ETDCFs and the dynamic ETDCFs of the slow particles increase with time in a concurrent manner. This suggests that the clustering of particles tends to build up dynamically correlated slow particles in the plane transverse to the lanes. The ETDCFs can be measured for colloidal systems by directly following the particle motion by video-microscopy and may be useful to understand the patterns out of equilibrium.

Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents  ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents  -3/2 and  -5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

Glass Stability Changes the Nature of Yielding under Oscillatory Shear

We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft materials to fatigue failure in metallic glasses.

Shear Bands Topology in the Deformed Bulk Metallic Glasses

Recent experimental studies revealed the presence of Volterra dislocation-type long-range elastic strain/stress field around a shear band (SB) terminated in a bulk metallic glass (BMG). The corollary from this finding is that shear bands can interact with these stress fields. In other words, the mutual behaviour of SBs should be affected by their stress fields superimposed with the external stresses. In order to verify this suggestion, the topography of the regions surrounding SBs terminated in the BMGs was carefully analysed. The surfaces of several BMGs, deformed by compression and indentation, were investigated with a high spatial resolution by means of scanning white-light interferometry (SWLI). Along with the evidence for the interaction between SBs, different scenarios of the SB propagation have been observed. Specifically, the SB path deviation, mutual blocking, and deflection of SBs were revealed along with the significant differences between the topologies of the mode II (in-plane) and mode III (out of plane) SBs. While the type II shear manifests a linear propagation path and a monotonically increasing shear offset, the type III shear is associated with a curved, segmented path and a non-monotonically varying shear offset. The systematic application of the “classic” elastic Volterra’s theory of dislocations to the behaviour of SBs in BMGs provides new insight into the widely reported experimental phenomena concerning the SB morphology, which is further detailed in the present work.

Steady-state rheology and structure of soft hybrid mixtures of liquid crystals and magnetic nanoparticles

Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, λ, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered values of λ. At low and intermediate values of λ, a crossover from Newtonian to non-Newtonian behavior is observed as the rate of applied shear is increased. In contrast, for large values of λ, such a crossover is not observed within the range of shear rates considered. Also, the extent of the non-Newtonian regime increases as λ is increased. These features can be understood via the shear-induced changes of the microstructure. In particular, the LCs display a shear-induced isotropic-to-nematic transition at large shear rates with a shear-rate dependent degree of nematic ordering. The DSS show a shear-induced nematic ordering only for large values of λ, where the particles self-assemble into chains. Moreover, at large λ and low shear rates, our simulations indicate that the DSS form ferromagnetic domains.

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

The effect of periodic shear on strain localization in disordered solids is investigated using molecular dynamics simulations. We consider a binary mixture of one million atoms annealed to a low temperature with different cooling rates and then subjected to oscillatory shear deformation with a strain amplitude slightly above the critical value. It is found that the yielding transition occurs during one cycle but the accumulation of irreversible displacements and initiation of the shear band proceed over larger number of cycles for more slowly annealed glasses. The spatial distribution and correlation function of nonaffine displacements reveal that their collective dynamics changes from homogeneously distributed small clusters to a system-spanning shear band. The analysis of spatially averaged profiles of nonaffine displacements indicates that the location of a shear band in periodically loaded glasses can be identified at least several cycles before yielding. These insights are important for the development of novel processing methods and prediction of the fatigue lifetime of metallic glasses.

Nucleation Theory for Yielding of Nearly Defect-Free Crystals: Understanding Rate Dependent Yield Points

Experiments and simulations show that when an initially defect-free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called yield point. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small nonuniversal exponent. We reanalyze a representative set of published data on nanometer sized, mostly defect-free Cu, Ni, and Au crystals in light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid. The single relation derived here, which is not a power law, explains data covering 15 orders of magnitude in timescales.

Microscopic precursors of failure in soft matter

The mechanical properties of soft matter are of great importance in countless applications, in addition of being an active field of academic research. Given the relative ease with which soft materials can be deformed, their non-linear behavior is of particular relevance. Large loads eventually result in material failure. In this Perspective article, we discuss recent work aiming at detecting precursors of failure by scrutinizing the microscopic structure and dynamics of soft systems under various conditions of loading. In particular, we show that the microscopic dynamics is a powerful indicator of the ultimate fate of soft materials, capable of unveiling precursors of failure up to thousands of seconds before any macroscopic sign of weakening.

Probing the Degree of Heterogeneity within a Shear Band of a Model Glass

Recent experiments provide evidence for density variations along shear bands in metallic glasses with a length scale of a few hundred nanometers. Via molecular dynamics simulations of a generic binary glass model, here we show that this is strongly correlated with variations of composition, coordination number, viscosity, and heat generation. Individual shear events along the shear band path show a mean distance of a few nanometers, comparable to recent experimental findings on medium range order. The aforementioned variations result from these localized perturbations, mediated by elasticity.

Effect of Pinning on the Yielding Transition of Amorphous Solids

Using numerical simulations, we have studied the yielding response, in the athermal quasistatic 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 a 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 via a spatially homogeneous proliferation of localized events.

Percolation Phase Transition from Ionic Liquids to Ionic Liquid Crystals

Due to their complex molecular structures and interactions, phase behaviors of complex fluids are quite often difficult to be identified by common phase transition analysis methods. Percolation phase transition, on the other hand, only monitors the degree of connection among particles without strict geometric requirements such as translational or orientational order, and thus suitable for pinpointing phase transitions of complex fluids. As typical complex fluids, ionic liquids (ILs) exhibit phases beyond the description of simple liquid theories. In particular, with an intermediate cationic side-chain length, ILs can form the nanoscale segregated liquid (NSL) state, which will eventually transform into the ionic liquid crystal (ILC) structure when the side chains are adequately long. However, the microscopic mechanism of this transformation is still unclear. In this work, by means of coarse-grained molecular dynamics simulation, we show that, with increasing cationic side-chain length, some local pieces of non-polar domains are gradually formed by side chains aligned in parallel inside the NSL phase, before an abrupt percolation phase transition happens when the system transforms into the ILC phase. This work not only identifies that the NSL to ILC phase transition is a critical phenomenon, but also demonstrates the importance of percolation theory to complex fluids.

Shear-Transformation Zone Activation during Loading and Unloading in Nanoindentation of Metallic Glasses

Using molecular dynamics simulation, we study nanoindentation in large samples of Cu–Zr glass at various temperatures between zero and the glass transition temperature. We find that besides the elastic modulus, the yielding point also strongly (by around 50%) decreases with increasing temperature; this behavior is in qualitative agreement with predictions of the cooperative shear model. Shear-transformation zones (STZs) show up in increasing sizes at low temperatures, leading to shear-band activity. Cluster analysis of the STZs exhibits a power-law behavior in the statistics of STZ sizes. We find strong plastic activity also during the unloading phase; it shows up both in the deactivation of previous plastic zones and the appearance of new zones, leading to the observation of pop-outs. The statistics of STZs occurring during unloading show that they operate in a similar nature as the STZs found during loading. For both cases, loading and unloading, we find the statistics of STZs to be related to directed percolation. Material hardness shows a weak strain-rate dependence, confirming previously reported experimental findings; the number of pop-ins is reduced at slower indentation rate. Analysis of the dependence of our simulation results on the quench rate applied during preparation of the glass shows only a minor effect on the properties of STZs.

Precursors of fluidisation in the creep response of a soft glass

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

Inhomogeneity of Free Volumes in Metallic Glasses under Tension

In this work, the deformation of Zr₂Cu metallic glass (MG) under uniaxial tensile stress was investigated at the atomic level using a series of synchrotron radiation techniques combined with molecular dynamics simulation. A new approach to the quantitative detection of free volumes in MGs was designed and it was found that free volumes increase in the elastic stage, slowly expand in the yield stage, and finally reach saturation in the plastic stage. In addition, in different regions of the MG model, free volumes exhibited inhomogeneity under stress, in terms of size, density, and distribution. In particular, the expansion of free volumes in the center region was much more rapid than those in the other regions. It is interesting that the density of free volumes in the center region abnormally decreased with strain. It was revealed that the atomic-level stress between different regions may contribute to the inhomogeneity of free volumes under stress. In addition, the inhomogeneous change of free volumes during the deformation was confirmed by the evolution of local atomic shear strains in different regions. The present work provides in-depth insight into the deformation mechanisms of MGs.

On the effect of the thermostat in non-equilibrium molecular dynamics simulations

The numerical investigation of the statics and dynamics of systems in non-equilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium systems can be successfully adapted to out-of-equilibrium cases. This is especially true for thermostats. Indeed, even though thermostats developed to work under equilibrium conditions sometimes display good agreement with rheology experiments, their performance rapidly degrades beyond weak dissipation and small shear rates. Here we focus on gauging the relative performances of three thermostats, Langevin, dissipative particle dynamics, and Bussi-Donadio-Parrinello under varying parameters and external conditions. We compare their effectiveness by looking at different observables and clearly demonstrate that choosing the right thermostat (and its parameters) requires a careful evaluation of, at least, temperature, density and velocity profiles. We also show that small modifications of the Langevin and DPD thermostats greatly enhance their performance in a wide range of parameters.

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.

Transient dynamical responses of a charged binary colloid in an electric field

In a model system of oppositely charged colloids we study via Brownian dynamics simulation the dynamical response as the system approaches steady states upon application of a constant electric field. The system is known to form patterns of like charges in the transverse plane to the field that are elongated along the field as lanes. We show that an increase in structural heterogeneity leads to non-Gaussian tails in the probability distribution of particle displacements [self van Hove functions (self-vHfs)]. The self-diffusion coefficient depends upon the time of the observations and consequently indicates aging in the system. However, the anomalies in the self-vHfs and diffusion do not appear during the melting of the structures.

On the existence of thermodynamically stable rigid solids

Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field-strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

Evolution of the pore size distribution in sheared binary glasses

Molecular dynamics simulations are carried out to investigate mechanical properties and porous structure of binary glasses subjected to steady shear. The model vitreous systems were prepared via thermal quench at constant volume to a temperature well below the glass transition. The quiescent samples are characterized by a relatively narrow pore size distribution whose mean size is larger at lower glass densities. We find that in the linear regime of deformation, the shear modulus is a strong function of porosity, and the individual pores become slightly stretched while their structural topology remains unaffected. By contrast, with further increasing strain, the shear stress saturates to a density-dependent plateau value, which is accompanied by pore coalescence and a gradual development of a broader pore size distribution with a discrete set of peaks at large length scales.

Direct Observation of Percolation in the Yielding Transition of Colloidal Glasses

When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Because of the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow us to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of nonaffine deformation percolating at yielding. In agreement with percolation theory, the spanning cluster is fractal with a fractal dimension d_{f}≃2, and the correlation length diverges upon approaching the critical yield strain. These results indicate that percolation of highly nonaffine particles is the hallmark of the yielding transition in disordered glassy systems.

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.

Transient inhomogeneous flow patterns in supercooled liquids under shear

Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in their local dynamical properties. Using detailed molecular dynamics simulations, we find that for sufficiently low temperatures and sufficiently high shear rates supercooled liquids also show transient inhomogeneous flow patterns (shear banding) in the start-up of steady shear flow, similar to what has already been observed for many other soft glassy systems. We verify that the onset of transient shear banding coincides quite well with the appearance of a stress overshoot for temperatures in the supercooled regime. We find that the slower bands adapt less well to the imposed deformation and therefore accumulate higher shear stresses compared to the fast bands at comparable local shear rates. Our results also indicate that the shear rates of the fast and slow bands are adjusted such that the local dissipation rate is approximately the same in both bands.

The yielding transition in amorphous solids under oscillatory shear deformation

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, 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 transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

The onset of yielding can be difficult to define unambiguously for amorphous materials. Here the authors undertake computer simulations of model glasses of varying system sizes and show that, under oscillatory shear, they exhibit a sharp transition independent of preparation history.

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.