Second gradient viscoelastic fluids: Dissipation principle and free energies

G. Amendola, M. Fabrizio, J. M. Golden

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a appropriate modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they differ from the standard Graffi conditions. Various free energy functionals, which are well-known in relation to simple materials, are generalized so that they apply to this fluid. In particular, expressions for the minimum free energy and a more recently introduced explicit functional of the minimal state are proposed. Derivations of various formulae are abbreviated if closely analogous proofs already exist in the literature.

    Original languageEnglish
    Pages (from-to)1859-1868
    Number of pages10
    JournalMeccanica
    Volume47
    Issue number8
    DOIs
    Publication statusPublished - Nov 2012

    Keywords

    • Free energy
    • Mechanical power
    • Non-simple fluid
    • Thermodynamic constraints
    • Viscoelasticity

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