We present results on a series of two-dimensional atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events. The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix. The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed. Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear--so-called "shear bands"--found in related studies. The slip lines give rise to particular scalings with system length of various measures of event size. Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions. The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials.

We show that, in the athermal quasi-static deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a divergence of elastic constants. A normal mode analysis of the non-affine elastic displacement field allows us to clarify its relation to the zero-frequency mode at the onset of failure and to the crack-like pattern which results from the subsequent relaxation of energy.Experiments on nanoindentation of metallic glasses [1], on granular materials [2] and on foams [3], demonstrate that at very low temperature and strain rates, the microstructural mechanisms of deformation involve highly intermittent stress fluctuations. These fluctuations can be accessed in molecular dynamics simulations, but are best characterized numerically via "exact" implementation of a-thermal quasi-static deformation: alternating elementary steps of affine deformation with energy relaxation [4] permits one to constrain the system to reside in a local energy minimum (inherent structure) at all times. As illustrated in figure 1, macroscopic stress fluctuations arise from a series of reversible (elastic) branches corresponding to deformation-induced changes of local minima. These branches are interrupted by sudden irreversible (plastic) events which occur when the inherent structure annihilates during a collision with a saddle point.[5] These transitions constitute the most elementary mechanism of deformation and failure for disordered materials at low temperature.Using this quasi-static protocol, recent studies of both elasticity [6] and plasticity [5], could identify important properties of elasto-plastic behavior which arise solely from the geometrical structure of the potential energy landscape. Tanguy et al [6] have observed that, following reversible (elastic) changes of the inherent structures, molecules undergo large scale non-affine displacements. They have shown these non-affine displacements to be related to the breakdown of classical elasticity at small scales and to quantitative differences between measured Lamé constants and their Born approximation. Malandro and Lacks [5] have shown that the destabilization of a minimum occurs through shear-induced collision with a saddle. At the collision, a single normal mode sees its eigenvalue going to zero. Building on this work, we studied the irreversible (plastic) event following the disappearance of an inherent structure: subsequent material deformation in search of a new minimum involves non-local displacement fields -in the likeness of nascent cracks-controlled by long-range elastic interactions. [7] Several molecular displacement fields thus appear to be closely related to the geometrical structure of the potential energy landscape: (i) non-affine displacements along elastic branches, (ii) the single normal mode controlling the annihilation of an inherent structure, and (iii) the overall deformation occurring during an irreversible event. In order to piece together a complete picture of elasto-plasticity at the nanoscale, we need ...

We study exact results concerning the non-affine displacement fields observed by Tanguy et al

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

The normal modes and the density of states (DOS) of any material provide a basis for understanding its thermal and mechanical transport properties. In perfect crystals, normal modes are plane waves, but they can be complex in disordered systems. We have experimentally measured normal modes and the DOS in a disordered colloidal crystal. The DOS shows Debye-like behavior at low energies and an excess of modes, or Boson peak, at higher energies. The normal modes take the form of plane waves hybridized with localized short wavelength features in the Debye regime but lose both longitudinal and transverse plane-wave character at a common energy near the Boson peak.

We present the results of numerical simulations of an atomistic system undergoing plastic shear flow in the athermal, quasistatic limit. The system is shown to undergo cascades of local rearrangements, associated with quadrupolar energy fluctuations, which induce system-spanning events organized into lines of slip oriented along the Bravais axes of the simulation cell. A finite size scaling analysis reveals subextensive scaling of the energy drops and participation numbers, linear in the length of the simulation cell, in good agreement with the observed real-space structure of the plastic events.PACS numbers: 81.40.Lm,62.20.Fe,62.20.Mk,46.50.+a The recent years have seen an important number of numerical and theoretical studies of plasticity in amorphous materials. The microscopic picture of plastic deformations which emerges from these studies, however, is still incomplete... at best, fragmented. Numerical evidence that plastic deformation involves highly heterogenous displacements of molecules led, early on, to the concept of "shear transformation zones", which are expected to play, for amorphous solids, the rôle of defects in crystals . This line of research should be contrasted with the phase space interpretation of plastic deformation recently proposed by Malandro and Lacks,[9] on the basis of the inherent structure formalism.[10] These authors study shear induced changes in the potential energy landscape, and the consequences of such changes on the macroscopic mechanical behavior of glasses. In order to isolate these effects, Malandro and Lacks consider the quasistatic deformation of an amorphous material at zerotemperature, a protocol which has been used since early numerical studies as a means to bypass intrinsic limitations of molecular dynamics algorithms.[1] For small deformations, the system follows shear induced changes of a local minimum (inherent structure) in the potential energy landscape. Elementary catastrophic events occur when the local minimum in which the system resides annihilates during a shear-induced collision with a saddle point. The deformation of an amorphous material thus involves a series of reversible (elastic) branches intersected by plastic rearrangements (see figure 1).The inherent structure formalism provides a precise definition of an elementary plastic rearrangement, but several questions arise about the spatial organization of these transitions: Are plastic events related to shear transformation zones and quadrupolar energy fluctuations? Do they involve spatially localized dynamical structures? If not, how do these structures scale with system size? Conflicting answers to these questions can be found in the literature. From measurements of participation ratio, Malandro and Lacks indicate that the elementary rearrangements they observe are localized.[9] Durian and coworkers, for a model of foam (athermal by construction), observe a power-law distribution of energy drops at small strain rates, but with a systemsize independent cut-off, indicating that no scaling behavior i...

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval ∆γ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small ∆γ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as ∆γ increases to about .03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest ∆γ studied.

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.