Shear band dynamics from a mesoscopic modeling of plasticity

TL;DR

This paper presents a mesoscopic model of plasticity to study shear band formation and dynamics in disordered materials, explaining transient behaviors, stabilization mechanisms, and phenomena like stick-slip relevant to seismic activity.

Contribution

It introduces a mesoscopic modeling approach that captures transient shear band growth, stabilization by relaxation effects, and complex dynamics such as stick-slip, aligning with experimental and atomistic simulation results.

Findings

Transient shear bands follow a t^1/2 thickness growth law.

Relaxation effects stabilize shear band width depending on strain-rate.

Low strain-rate dynamics include stick-slip behavior relevant to seismic phenomena.

Abstract

The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational (aging) effects. In the absence of relaxational effects the model displays a monotonously increasing dependence of stress on strain-rate, and stationary shear bands do not occur. However, in start up experiments transient (although long lived) shear bands occur, that widen without bound in time. I investigate this transient effect in detail, reproducing and explaining a t^1/2 law for the thickness increase of the shear band that has been obtained in atomistic numerical simulations. Relaxation produces a negative sloped region in the stress vs. strain-rate curve that stabilizes the formation of shear bands of a well defined width, which is a function of strain-rate. Simulations at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin shear bands that has relevance in the study of seismic phenomena. In addition, other non-stationary processes, such as stop-and-go, or strain-rate inversion situations display a phenomenology that matches very well the results of recent experimental studies.