Minimal States and Periodic Histories

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 18 in Thermodynamics of Materials with Memory, 2021, pp 427-443 from Springer

Abstract: Abstract Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. State minimal functional of Using this condition and results on constructing free energy functionals in Chap. 17 , it is shown that if the kernel of the rate of dissipation functional is given by sums of products, the associated free energy functional is a FMS. Free energy functional of minimal state Because this condition is linear rather than a quadratic, it is easier to explore and to apply in new contexts.

Date: 2021
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DOI: 10.1007/978-3-030-80534-0_18

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