Elastic avalanches reveal marginal behaviour in amorphous solids

TL;DR

This paper investigates the scale-free plastic avalanches in amorphous solids, revealing that their behavior aligns with mean field predictions and indicating marginal stability in the elastic regime of glass-forming systems.

Contribution

It provides the first characterization of avalanche distributions in simple glass models, confirming mean field predictions and demonstrating marginal stability in the elastic regime.

Findings

Avalanche size distribution matches mean field predictions.

Scaling relations hold in the elastic regime.

Marginal stability persists in the thermodynamic limit.

Abstract

Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.