Shear-Transformation-Zone Theory of Yielding in Athermal Amorphous Materials

TL;DR

This paper uses the shear-transformation-zone (STZ) theory to analyze yielding in athermal amorphous materials, revealing that the transition is not truly critical despite Herschel-Bulkley-like rheologies.

Contribution

It introduces an elementary STZ-based framework focusing on effective disorder temperature to clarify the nature of yielding transitions.

Findings

Yielding transitions resemble critical phenomena but are not truly critical.

Correlation length grows rapidly but saturates near the yield point.

Herschel-Bulkley rheologies are broadly observed but do not imply criticality.

Abstract

Yielding transitions in athermal amorphous materials resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. In particular, there is a correlation length that grows rapidly, but ultimately saturates near the yield point.