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

Influence of Density and Pressure on Glass Formation in the Kob-Andersen Model

We systematically study glass formation in the well-known Kob-Andersen model over a wide range of densities and pressures as a basis for judging the "universality" of glass formation through a comparison to a recent systematic study of model polymeric glass-forming liquids. Our purpose is to establish general characteristics of glass formation, to identify new relations, and to discern which properties of glass-forming liquids are material-specific and which are "universal." To this end, we analyze a number of characteristic properties of glass formation, such as the structural relaxation time, self-diffusion coefficient, viscosity, characteristic temperatures, and fragility. We also consider a suite of properties presumably related to dynamic heterogeneity in an attempt to better understand its relation to structural relaxation. We demonstrate that the glassy dynamics in the Kob-Andersen model exhibit many of the essential trends observed in polymeric glass-forming liquids, pointing to a remarkable "universality" of many aspects of glass formation.

Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays

We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.

Characteristics and correlations of nonaffine particle displacements in the plastic deformation of athermal amorphous materials

When an amorphous solid is deformed homogeneously, it exhibits heterogeneous plastic instabilities with a localized cooperative rearrangement of a cluster of particles in response. The heterogeneous behavior plays an important role in deciding the mechanical properties of amorphous solids. In this paper, we employ computer simulations to study the characteristics and the spatial correlations of these clusters characterized by their non-affine displacements in amorphous solids under simple shear deformation in the athermal quasistatic limit. The clusters with large displacements are found to be homogeneously distributed in space in the elastic regime, followed by a localization within a system-spanning shear band after yielding. The distributions of the displacement field exhibit a power-law nature in the elastic regime with an exponential cutoff post yielding. The non-affine displacements show strong spatial correlations, which become long-ranged with increasing strain. From our results, it is evident that the decay of the correlation functions is exponential in nature in the elastic regime. The yielding transition is marked by an abrupt change in the decay after which it is well described by a power-law with an exponential cutoff. These results demonstrate a scale-free character of non-affine correlations in the steady flow regime. These results are found to be robust and independent of the strain window over which the total non-affine displacement is calculated.

Forced deterministic dynamics on a random energy landscape: Implications for the physics of amorphous solids

The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.

Rheological similarities between dense self-propelled and sheared particulate systems

Different from previous modeling of self-propelled particles, we develop a method to propel particles with a constant average velocity instead of a constant force. This constant propulsion velocity (CPV) approach is validated by its agreement with the conventional constant propulsion force (CPF) approach in the flowing regime. However, the CPV approach shows its advantage of accessing quasistatic flows of yield stress fluids with a vanishing propulsion velocity, while the CPF approach is usually unable to because of finite system size. Taking this advantage, we realize cyclic self-propulsion and study the evolution of the propulsion force with the propelled particle displacement, both in the quasistatic flow regime. By mapping the shear stress and shear rate to the propulsion force and propulsion velocity, we find similar rheological behaviors of self-propelled systems to sheared systems, including the yield force gap between the CPF and CPV approaches, propulsion force overshoot, reversible-irreversible transition under cyclic propulsion, and propulsion bands in plastic flows. These similarities suggest underlying connections between self-propulsion and shear, although they act on systems in different ways.

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.

Annealing and rejuvenation in a two-dimensional model amorphous solid under oscillatory shear

We study the annealing and rejuvenation behavior of a two-dimensional amorphous solid model under oscillatory shear. We show that, depending on the cooling protocol used to create the initial configuration, the mean potential energy can either decrease or increase under subyield oscillatory shear. For post-yield oscillatory shear, the mean potential energy increases and is independent on the initial conditions. We explain this behavior by modeling the dynamics using a simple model of forced dynamics on a random energy landscape and show that the model reproduces the qualitative behavior of the mean potential energy and mean-square displacement observed in the particle based simulations. This suggests that some important aspects of the dynamics of amorphous solids can be understood by studying the properties of random energy landscapes and without explicitly taking into account the complex real-space interactions which are involved in plastic deformation.

Critical diffusivity in the reversibility-irreversibility transition of amorphous solids under oscillatory shear

Recently it was shown that under oscillatory shear at zero temperature an amorphous solid transitions from asymptotically periodic to asymptotically diffusive steady-state at a critical maximal strain amplitude. Current understanding of the physics behind this transition is lacking. Here we show, using computer simulations, evidence that the diffusivity of the vector of coordinates of the particles comprising an amorphous solid, when subject to oscillatory shear, undergoes a second order phase transition at the reversibility-irreversibility transition point. We explain how such a transition is consistent with dissipative forced dynamics on a complex energy landscape, such as is known to exist in amorphous solids. We demonstrate that as the forcing increases, more and more state-space volume becomes accessible to the system, making it less probable for the state-space trajectory of the system to self-intersect and form a limit-cycle, which explains the slowing-down observed at the transition.

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.