Schematic Mode Coupling Theory of Glass Rheology: Single and Double Step Strains

TL;DR

This paper uses schematic mode coupling theory to analyze the rheology of glasses under single and double step strains, revealing residual stress and plastic deformation effects not captured by traditional models.

Contribution

It introduces a MCT-based constitutive equation that captures nontrivial stress responses and distinguishes between instantaneous and ramped strains in glass rheology.

Findings

Residual stress persists after opposite step strains, indicating plasticity.

Fast ramps differ from instantaneous steps, affecting stress response.

The model highlights the role of irreversible plastic rearrangements.

Abstract

Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of plastic deformation. We also discuss the distinction between hypothetically instantaneous step strains and fast ramps. These are not generally equivalent in our MCT approach, with the latter more likely to capture the physics of experimental `step' strains. The distinction points to the different role played by reversible anelastic, and irreversible plastic rearrangements.