Local elasticity map and plasticity in a model Lennard-Jones glass

Abstract

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Visualizing the strain evolution during the indentation of colloidal glasses

“…At the particle scale, however, the deformation should be largely affected by the heterogeneous structure of the glass. As shown recently by simulations [22] and atomic force microscopy experiments [23], the heterogeneity of the amorphous structure leads to strong variations of the elastic moduli; this variation should bias rearrangements to occur at locations that are structurally weak [24,25]. This is also suggested by free volume [26] and shear transformation zone theories [27] that relate plastic deformation to the structure via a structural parameter.…”

Shear transformation zone dynamics model for metallic glasses incorporating free volume as a state variable

“…For example, the present model creates and annihilates excess free volume locally; future work must focus on the diffusion of this free volume rather than the creation and annihilation thereof. Additionally, the excess free volume is a phenomenological variable like those used in most of the mesocale models [23, 31 -32, 41]; one could develop similar approaches that connect to alternative state variables such as local elastic properties [42], local bonding such as icosahedral or non--icosahedral effects [14]; or dynamical state variables such as an effective disorder temperature [43 -45]. Each of these state variables provide something unique to describe structural disorder of glasses, and the complex structural evolution in metallic glasses provides freedom in the selection and description of variables to describe similar behaviors.…”

Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses

“…In amorphous solids, however, geometric structural parameters are not obviously connected to regions that later rearrange [2], hampering a priori identification of fragile regions. Recent numerical simulations suggest that the spatial distribution of low-frequency phonon modes may be correlated with irreversible rearrangements in glasses [3,4] and that the quasilocalized low-frequency vibrational modes often observed in glasses [5] play a role in glass mechanical response [6][7][8]. In a related vein, experiments in vibrated granular packings find that when cracks begin to appear, particles are likely to move in the direction of the polarization vectors of the lowest-frequency modes [4].…”