Elastoviscoplastic rheology and aging in a simplified soft glassy constitutive model

Abstract

Yield stress fluids display a rich rheological phenomenology. Beyond the defining existence of a yield stress in the steady state flow curve, this includes in many materials rather flat viscoelastic spectra over many decades of frequency in small amplitude oscillatory shear; slow stress relaxation following the sudden imposition of a small shear strain; stress overshoot in shear startup; logarithmic or sublinear power law creep following the imposition of a shear stress below the yield stress; creep followed by yielding after the imposition of a shear stress above the yield stress; richly featured Lissajous-Bowditch curves in large amplitude oscillatory shear; a Bauschinger effect, in which a material's effective yield strain is lowered under straining in one direction, following a preceding strain in the opposite direction; hysteresis in up-down shear rate sweeps; and (in some materials) thixotropy and/or rheological ageing. A key challenge is to develop a constitutive model that contains enough underlying mesoscopic physics to have meaningful predictive power for the full gamut of rheological behaviour just described, with only a small number of model parameters, and yet is simple enough for use in computational fluid dynamics to predict flows in complicated geometries, or complicated flows that arise due to spontaneous symmetry breaking instabilities even in simple geometries. Here we introduce such a model, motivated by the widely used soft glassy rheology model, and show that it captures all the above rheological features.

Slide‐Hold‐Slide Protocols and Frictional Healing in Discrete Element Method (DEM) Simulations of Granular Fault Gouge

“…Additional future research may explore recent definitions of state variable for amorphous materials (e.g., D. Richard et al., 2021) in the context of elastoviscoplastic rheology for soft glassy materials (e.g., Fielding, 2020). Also, our study here has been focused on the stress relaxation and healing behavior of a sheared granular layer that shows velocity‐strengthening frictional behavior.…”

Criterion for Fingering Instabilities in Colloidal Gels

“…Future work should aim at placing the criterion for fingering instabilities in the context of the activated-like yielding scenario that currently prevails in the literature [52][53][54]. Within that framework, our findings could be relevant for interpreting recent yielding experiments in colloidal gels controlled by ultrasonic vibrations [55], and constitute a benchmark set of experimental data to test glassy constitutive models [56].…”

Fluidisation of yield stress fluids under vibration

“…Understanding the detailed mechanics of yielding is key to the development of accurate constitutive models, which can in turn be applied to predict flow in a variety of practically-relevant configurations. Such models may be derived from the microscopic dynamics [16] or the relationship between stress, strain and rate of strain, formulated at a macroscopic scale to capture the mechanics observed experimentally. Arguably the most successful constitutive model to date is the Saramito model [28], which treats the material as a linear viscoelastic solid (with a characteristic relaxation time) for stresses below yield and an elastoviscoplastic fluid with a Herschel-Bulkley viscosity above yield.…”