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Minimal States and Periodic Histories

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

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.

Suggested Citation

  • Giovambattista Amendola & Mauro Fabrizio & John Golden, 2021. "Minimal States and Periodic Histories," Springer Books, in: Thermodynamics of Materials with Memory, edition 2, chapter 0, pages 427-443, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-80534-0_18
    DOI: 10.1007/978-3-030-80534-0_18
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