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