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Free energies in a general non-local theory of a material with memory

Giovambattista Amendola

Dipartimento di Matematica Applicata, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

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Mauro Fabrizio

Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy

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, and

John Murrough Golden

School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

Corresponding author.

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https://doi.org/10.1142/S0218202513500760Cited by:6 (Source: Crossref)

Abstract

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are given for these quantities in the case of sinusoidal histories.

Keywords:

AMSC: 80A17, 74A15, 74A30

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