Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids Academic Article uri icon

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 CauchyGreen 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.

published proceedings

  • FLUIDS

altmetric score

  • 0.5

author list (cited authors)

  • Prusa, V., & Rajagopal, K. R.

citation count

  • 3

complete list of authors

  • Průša, Vít||Rajagopal, KR

publication date

  • March 2021

publisher

published in