A Minimal Nonlocal Theory of Thixotropic Flow

TL;DR

This paper introduces a minimal coupled model of nonlocal fluidity and structural memory to better describe history-dependent flow behaviors in dense amorphous materials, capturing hysteresis and delayed yielding.

Contribution

The paper presents a novel coupling of memory and nonlocality in a continuum model, enabling simultaneous representation of aging, rejuvenation, and spatial cooperativity in rheology.

Findings

Reproduces hysteresis in shear-rate sweeps

Captures delayed yielding in creep tests

Shows nonlocality alone cannot encode history

Abstract

Dense amorphous materials exhibit both nonlocal flow cooperativity and pronounced history dependence, yet existing continuum models capture only one of these features at a time. Nonlocal rheologies are intrinsically memoryless, while thixotropic models remain local. Here we introduce a coupling between structural memory and nonlocal fluidity to include aging and rejuvenation in nonlocal granular fluidity. The resulting model reproduces hysteresis in shear-rate sweeps and delayed yielding in creep, while preserving nonlocal flow profiles. By introducing memory augmented non local granular fluidity, MNGF, we show that nonlocality alone cannot encode history, and memory alone cannot encode spatial cooperativity, but their coupling is essential and minimal. These results demonstrate that memory and nonlocality must be treated jointly to describe history dependent flows, and provide a unified framework for modeling time-dependent rheology in dense amorphous materials.