Comptes Rendus
A review of implicit algebraic constitutive relations for describing the response of nonlinear fluids
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 703-720.

We review the class of implicit algebraic constitutive relations for fluids which includes in its ambit those whose material properties depend on the invariants of the stress, the symmetric part of the velocity gradient, as well as their mixed invariants. Such constitutive relations can describe the response of complex fluids whose material properties depend on the mechanical pressure, shear rate, etc. The class of models under consideration can describe the non-monotone relationship between the shear stress and the shear rate observed in experiments on colloids, as well as other novel response characteristics of non-Newtonian fluids. Constitutive relations for power-law fluids, generalized Stokesian fluids and Piezo-viscous fluids are special sub-classes of the class of fluids considered herein.

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DOI: 10.5802/crmeca.180
Keywords: implicit constitutive relations, colloids, stress power-law fluids, non-monotone stress-shear rate relations, monotone graphs

Kumbakonam Rajagopal 1

1 Department of Mechanical Engineering, Texas A& M University, College Station, TX 77845, United States
License: CC-BY 4.0
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Kumbakonam Rajagopal. A review of implicit algebraic constitutive relations for describing the response of nonlinear fluids. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 703-720. doi : 10.5802/crmeca.180. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.180/

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