Strain localization in a shear transformation zone model for amorphous solids

TL;DR

This paper presents a mean-field STZ model for amorphous solids that captures strain localization phenomena, matches simulation data, and predicts conditions for shear band formation based on initial states and strain rate.

Contribution

The study introduces a continuum STZ model that explains strain localization and shear band formation, linking instability growth to nonlinear energy dissipation and initial conditions.

Findings

Model fits simulation data of shear localization

Perturbation growth leads to shear band formation under certain conditions

Shear band width depends on strain rate, not a fixed diffusion length

Abstract

We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates solutions that fit the data,exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.