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.
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Soft Matter, Royal Society of Chemistry, 2017, 13 (26), pp.4653 - 4660. 〈10.1039/C6SM02702D〉
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Elisabeth Agoritsas, Kirsten Martens. Nontrivial rheological exponents in sheared yield stress fluids. Soft Matter, Royal Society of Chemistry, 2017, 13 (26), pp.4653 - 4660. 〈10.1039/C6SM02702D〉. 〈hal-01563960〉

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