A constitutive model for bentonite–water mixture and the effect of wall slip boundary conditions on its mechanical response

Sumith, S.; Kannan, K.; Shankar, K.

doi:10.1016/j.ijnonlinmec.2019.103318

Cited by 4 publications

(1 citation statement)

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“…Our basic framework is based on the concept of evolving natural configuration (see Eckart [66] and Rajagopal and Srinivasa [67]) that has been successfully applied in various settings; see for example Málek [74] or Sumith et al [75] to name a few (for other approaches to the mathematical modeling of viscoelastic rate-type fluids, see Leonov [76,77], Wapperom and Hulsen [78] or the GENERIC framework; see Grmela and Öttinger [79], Öttinger and Grmela [80] and Pavelka et al [81]).…”

Section: Viscoelastic Rate-type Fluidsmentioning

confidence: 99%

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

Průša

Rajagopal

2021

Fluids

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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.

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