Unified Microscopic Theory of Stress Relaxation, Structural Evolution, and Memory Effects in Dense Glass Forming Brownian Suspensions After Flow Cessation

TL;DR

This paper develops a microscopic statistical mechanical theory to predict structural and stress recovery in dense glass-forming Brownian suspensions after flow cessation, capturing complex relaxation behaviors and memory effects.

Contribution

It introduces a unified microscopic framework that models coupled structural and stress evolution post-flow cessation in dense colloidal suspensions, incorporating activated dynamics and elastic backflow.

Findings

Captures exponential, stretched exponential, and power-law stress relaxation behaviors.

Explains emergence of residual stresses and aging phenomena.

Describes decoupling of structural relaxation from stress relaxation.

Abstract

The re-solidification of amorphous solids after mechanically driven yielding from a nonequilibrium state is a fundamental soft matter science problem of broad relevance in materials science, with implications for material strength, processing, and printing-based additive manufacturing. We present a microscopic statistical mechanical theory that predicts in a unified manner the coupled time evolutions of structural and stress recovery following shear cessation from a mechanically prepared nonequilibrium state. The approach is built on recent advances in understanding activated dynamics in Brownian systems under both quiescent and startup continuous shear conditions. A particle-level microrheological model framework self-consistently incorporates stress generation, constraint softening due to external mechanical forces and structural deformation. After flow cessation, the theory captures the re-building of kinetic constraints and activation barriers over time that underlie structural recovery, stress relaxation, and re-solidification through dynamic relaxation and an elementary form of convective elastic backflow. The ideas are general for particle-based materials, and quantitatively applied to dense hard-sphere Brownian colloidal suspensions which also serve as a foundational paradigm for glass forming materials where thermal fluctuations are important. The theory properly captures the rich range of stress relaxation behaviors observed experimentally that evolve from exponential, to stretched exponential, to fractional power law in form with increasing packing fraction. A microscopic understanding is achieved of the emergence of apparent residual stresses on laboratory timescales, power-law endless aging, sigmoidal recovery of the elastic modulus, pre-shear-rate-dependent memory effects, and a two-step structural relaxation process that can become decoupled from stress relaxation.