Amorphous systems in athermal, quasistatic shear

Abstract

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.

The jamming scenario—an introduction and outlook

“…As the sample is compressed or sheared, it will eventually go unstable and rearrange into a new configuration. At zero temperature, this instability is governed by some quasi-localized mode in the system that goes "soft so that its frequency is pushed down until it reaches zero [113]. At this point, the sample moves into a new configuration.…”

“…However, the failure often occurs in the form of rather localized rearrangement events rather than via a longrange catastrophic collapse [56,58,59]. Since the system goes unstable when the frequency of a mode reaches zero, it is possible to identify a rearrangement with the lowest-frequency mode just before the rearrangement [113]. However, ideally one would like to predict well in advance where failure will occur, even in large systems with many plane-wave-like modes at low frequencies.…”

“…This result, together with previous observations [54][55][56], should have important consequences for the dynamics and instabilities that occur as the temperature is raised from zero, the system is compressed, or a shear stress is applied. One would expect these modes to shift downwards to zero frequency under the last two circumstances [57] and to give rise to highly heterogeneous deformations in the sample. These could be the underlying mechanism for the localized deformations postulated in the picture of shear transformation zones [58,59].…”

Plastic response of a two-dimensional amorphous solid to quasistatic shear: Transverse particle diffusion and phenomenology of dissipative events

“…The associated inter-zone elastic couplings should be responsible for the "autocatalytic avalanches" [5,12] or flip cascades [4,13] constituting the system-size dependent plastic events, which we believe to be precisely the non-permanent shear bands invoked in ref. [10].…”

“…The distribution of stress drops is broad and systemsize dependent. In their study on a 2D LJ glass, Maloney and Lemaitre [4] were able to analyze them in terms of cascades of elementary events, which we will term "flips". Each such flip involves both the strong rearrangement of a small cluster ( ∼ a few atoms), and the appearance of an associated quadrupolar elastic field.…”