Constructing Free Energies for Materials with Memory

Giovambattista Amendola, Mauro Fabrizio and John Golden
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Giovambattista Amendola: University of Pisa, Dipartimento di Matematica
Mauro Fabrizio: University of Bologna, Dipartimento di Matematica
John Golden: Technological University - Dublin, Grangegorman Campus

Chapter Chapter 17 in Thermodynamics of Materials with Memory, 2021, pp 385-426 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-80534-0_17

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