Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of soft glassy materials

Abstract

We study theoretically shear banding in soft glassy materials subject to large amplitude time-periodic shear flows, considering separately the protocols of large amplitude oscillatory shear strain, large amplitude square or triangular or sawtooth strain rate, and large amplitude oscillatory shear stress. In each case, we find shear banding to be an important part of the material's flow response for a broad range of values of the frequency $\omega$ and amplitude of the imposed oscillation. Crucially, and highly counterintuitively, in the glass phase this persists even to the lowest frequencies accessible numerically (that seems consistent with it persisting even when $\omega \to 0$), although the soft glassy rheology model we use has an underlying monotonic constitutive curve of shear stress as a function of shear rate, and is therefore unable to support shear banding as its steady state response at constant shear rate. We attribute this to the repeated competition, within each flow cycle, of glassy aging and flow rejuvenation. Besides reporting significant banding in the glass phase, where the flow curve has a yield stress, we also observe it at noise temperatures just above the glass point, where the flow curve is of power law fluid form. Thus, our results suggest a predisposition to shear banding in flows of even extremely slow time-variation, for both aging yield stress fluids, and for power law fluids with sluggish relaxation timescales. We show that shear banding can have a pronounced effect on the shape of the Lissajous-Bowditch curves that are commonly used to fingerprint complex fluids rheologically. We therefore counsel caution in seeking to compute such curves calculations that impose upfront a homogeneous shear flow, discarding the possibility of banding. We also analyze the stress response to the imposed strain waveforms in terms of a `sequence of physical processes'.

19 pages, 13 figures

References in corpus (13)

• Fingerprinting Soft Materials: A Framework for Characterizing Nonlinear Viscoelasticity
• Yielding and flow in adhesive and non-adhesive concentrated emulsions
• Strain localization in a shear transformation zone model for amorphous solids
• Evaluation of the "disorder temperature" and "free volume" formalisms via simulations of shear banding in amorphous solids
• On the existence of a simple yield stress fluid behavior
• Stress localization, stiffening and yielding in a model colloidal gel
• Shear banding, aging and noise dynamics in soft glassy materials
• A non-monotonic constitutive model is not necessary to obtain shear banding phenomena in entangled polymer solutions
• Rate dependent shear bands in a shear transformation zone model of amorphous solids
• Creep and flow of glasses: strain response linked to the spatial distribution of dynamical heterogeneities
• Transition from a simple yield stress fluid to a thixotropic material
• Influence of boundary conditions on yielding in a soft glassy material
• Investigation of shear banding in three-dimensional foams

Cited by in corpus (5)

• Glass stability changes the nature of yielding under oscillatory shear
• Deformation and flow of amorphous solids: An updated review of mesoscale elastoplastic models
• Elastoviscoplastic rheology and ageing in a simplified soft glassy constitutive model
• The Method of Harmonic Balance for the Giesekus Model under Oscillatory Shear
• Depinning dynamics of confined colloidal dispersions under oscillatory shear