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Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model. [ABSTRACT FROM AUTHOR]

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β∈R such that 0≤β≤1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0≤β≤1/2 and 1/2≤β≤1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to the order of the fractional derivative. Because the critical value 1/2 separates two different behaviors with different mechanical models, we propose to distinguish such different behavior as elasto-viscous case with 0≤β≤1/2 and visco-elastic case for 1/2≤β≤1. The motivations for this different definitions as well as the comparison with other existing mechanical models available in the literature are presented in the paper. [ABSTRACT FROM AUTHOR]