An extremal model for amorphous media plasticity

TL;DR

This paper introduces a simple two-dimensional extremal model for amorphous media plasticity, revealing complex correlations, anisotropic scaling laws, and a depinning transition related to material yield behavior.

Contribution

It presents a novel extremal model capturing the anisotropic and correlated nature of plastic deformation in amorphous materials, linking depinning transitions to yield stress.

Findings

Development of long-range correlations in slip events

Anisotropic scaling laws in plastic strain distribution

Identification of a depinning transition related to yield stress

Abstract

An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip events are shown to develop, leading to non-trivial and highly anisotropic scaling laws. In particular, the plastic strain is shown to statistically concentrate over a region which tends to align perpendicular to the displacement gradient. By construction, the model can be seen as giving rise to a depinning transition, the threshold of which (i.e. the macroscopic yield stress) also reveal scaling properties reflecting the localization of the activity.