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Constructing Free Energies for Materials with Memory

In: Thermodynamics of Materials with Memory

Author

Listed:
  • Giovambattista Amendola

    (University of Pisa, Dipartimento di Matematica)

  • Mauro Fabrizio

    (University of Bologna, Dipartimento di Matematica)

  • John Golden

    (Technological University - Dublin, Grangegorman Campus)

Abstract

We now discuss methods for deriving new functionals which have the properties of a free energy. Free energy properties Perhaps the central difficulty in constructing such quantities arises in making choices that ensure both a nonnegative quadratic form for the free energy and the rate of dissipation. Typically, if one chooses a suitable functional for the free energy, the associated rate of dissipation does not have the non-negativity property. A technique is presented in this chapter (see also [162]) which in effect reverses this procedure. We choose a nonnegative functional for the rate of dissipation Dissipation of energy rate of and derive formulae which give the associated free energy functional in terms of the dissipation rate kernel. It emerges that the resulting free energy has the required non-negativity property.

Suggested Citation

  • Giovambattista Amendola & Mauro Fabrizio & John Golden, 2021. "Constructing Free Energies for Materials with Memory," Springer Books, in: Thermodynamics of Materials with Memory, edition 2, chapter 0, pages 385-426, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-80534-0_17
    DOI: 10.1007/978-3-030-80534-0_17
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