Nontrivial rheological exponents in sheared yield stress fluids

Abstract

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

References in corpus (8)

• Scaling description of the yielding transition in soft amorphous solids at zero temperature
• Yielding and flow in adhesive and non-adhesive concentrated emulsions
• On the existence of a simple yield stress fluid behavior
• Non-local rheology in dense granular flows -- Revisiting the concept of fluidity
• Shear banding, aging and noise dynamics in soft glassy materials
• Relaxing in foam
• Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams
• On the relevance of disorder in athermal amorphous materials under shear

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• Thermally activated flow in models of amorphous solids
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• Mean field theory of yielding under oscillatory shear
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