The Minimum Free Energy for a Finite-Memory Material

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 15 in Thermodynamics of Materials with Memory, 2021, pp 339-348 from Springer

Abstract: Abstract In this chapter, based on work reported in [111], we derive an expression for the minimum free energy corresponding to a relaxation function with Relaxation function derivative finite-memory the special property that its derivative is nonzero over only a finite interval of time. It will be seen that there are special features associated with the analytic behavior of the frequency-space representation of such relaxation functions that render this a nontrivial extension, with unique features, of the general treatments presented in Chaps. 7 and 14 . This property of finite memory is of interest in the first instance because finite and infinite memories are not necessarily experimentally distinguishable; also, the assumption of infinite memory can lead to paradoxical results for certain problems.

Date: 2021
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DOI: 10.1007/978-3-030-80534-0_15

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