Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Energetic Constraints in a Minimal Theory

TL;DR

This paper derives a minimal energetic-based model for amorphous plasticity using shear-transformation-zone theory, capturing key features like yielding and strain softening, but highlighting the need for more complex internal variables.

Contribution

It introduces a simple quasilinear STZ model with an energetic coupling term, explaining plasticity phenomena and identifying its limitations.

Findings

Qualitatively reproduces yielding and strain softening.

Fails to capture some complex deformation behaviors.

Highlights need for additional internal degrees of freedom.

Abstract

We use energetic considerations to deduce the form of a previously uncertain coupling term in the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. As in the earlier versions of the STZ theory, the onset of steady deformation at a yield stress appears here as an exchange of dynamic stability between jammed and plastically deforming states. We show how an especially simple ``quasilinear'' version of this theory accounts qualitatively for many features of plasticity such as yielding, strain softening, and strain recovery. We also show that this minimal version of the theory fails to describe certain other phenomena, and argue that these limitations indicate needs for additional internal degrees of freedom beyond those included here.