Yield stress in amorphous solids: A mode-coupling theory analysis

TL;DR

This paper uses mode-coupling theory to analyze the yield stress in various amorphous solids, comparing theoretical predictions with numerical data, and discussing the theory's applicability and limitations.

Contribution

It applies mode-coupling theory to predict yield stress in different disordered solids and evaluates its accuracy and limitations across material classes.

Findings

Correctly predicts yield stress emergence in hard sphere glasses.

Captures qualitative growth of yield stress near close packing.

Fails to accurately describe solid behavior in soft and metallic glasses.

Abstract

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly non-linear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition, and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyse several classes of disordered solids, using simple models of hard sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the vibrational dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and non-linear rheology of amorphous materials.