Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids
TLDR
In this paper, the authors propose a new model for non-Newtonian viscoelastic fluids based on implicit constitutive relations, where the left Cauchy-Green tensor is expressed as a function of stress.Abstract:
Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory of nonlinear solids. Recently, new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of the elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy–Green tensor is expressed as a function of stress, is of interest. We show how to use this new perspective in the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalize to more complex settings wherein the classical approach might be impractical or even inapplicable.read more
Citations
More filters
Journal ArticleDOI
Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids
T. Bodnár,Adélia Sequeira +1 more
TL;DR: In this article , a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson-Segalman model under various settings is presented.
Journal ArticleDOI
A non-linear complementary energy-based constitutive model for incompressible isotropic materials
TL;DR: Inverse nonlinear stress-strain relations between the logarithmic Hencky strain tensor and the Cauchy stress tensor are derived for incompressible isotropic materials as discussed by the authors .
References
More filters
MonographDOI
Functions of Matrices: Theory and Computation
TL;DR: A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.
Journal ArticleDOI
On the Formulation of Rheological Equations of State
TL;DR: The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed in this article, where the right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material.
Journal ArticleDOI
Konsistenzmessungen von Gummi-Benzollösungen
TL;DR: In this article, the authors discuss the effect of konsistenzbestimmung durch Benutzung dieser Gleichung, der das verwendbare Werte fur alle praktischen Stromungsgeschwindigkeiten liefert and das sie die Notwendigekeit, sehr hohe Drucke anzuwenden, vermeidet.
Journal ArticleDOI
Dynamics and thermodynamics of complex fluids. I. Development of a general formalism
TL;DR: In this article, the GENERIC is formulated as a general equation for the nonequilibrium reversible-irreversible coupling (abbreviated as GIC) and its solutions are derived.
Related Papers (5)
On implicit constitutive relations for materials with fading memory
Perspectives on using implicit type constitutive relations in the modelling of the behaviour of non-Newtonian fluids
Adam Janečka,Vít Průša +1 more