Thermodynamics of a non-simple heat conductor with memory

Amendola, Giovambattista; Fabrizio, Mauro; Golden, John M.

doi:10.1090/s0033-569x-2011-01228-5

Cited by 8 publications

(14 citation statements)

References 22 publications

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“…Properties of the optimal future continuation 1 We draw attention to certain properties of the optimal future continuation. From 2 (8.12) and (8.24) 2 , it follows that Thus, the optimal continuation involves a sudden discontinuity at time t, the mag-10 nitude of which is related to the rate of dissipation, as we see from (8.25).…”

Section: 5mentioning

confidence: 99%

“…This is the condition that the processĊ i (t+s), i = 1, 2, s ∈ R + acting on each is the same. Note that it follows from (5.1) 1 that Σ (1) = Σ (2) where Σ (1) and Σ (2) are the dependent quantities (for example, stress tensors in mechanics)…”

mentioning

confidence: 99%

“…The 1 first two terms on the right yield, after integration, the integral term in (7.2) and the 2 last term is the memory integral in (3.20) 1 , multiplied in both cases by a factor 2.…”

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confidence: 99%

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

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Section: 5mentioning

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

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“…Recently Fabrizio, Lazzari and Nibbi [22], and Amendola, Fabrizio and Golden [23], proposed a new procedure to achieve generalizations of the laws of thermodynamics, which consists in expressing them in terms of internal powers. According to their suggestion, for some classes of nonlocal materials, an extension of first law of thermodynamics, and not only of second law, is necessary.…”

Section: Introductionmentioning

confidence: 99%

Entropy Principle and Recent Results in Non-Equilibrium Theories

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Ruggeri

et al. 2014

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We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

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“…Various steps in the derivations are omitted or abbreviated when they are closely analogous to developments in [3] (also [4]) for non-simple heat conductors.…”

Section: Introductionmentioning

confidence: 99%

Second gradient viscoelastic fluids: dissipation principle and free energies

Amendola

Fabrizio

Golden³

2012

Meccanica

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We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they differ from the standard Graffi conditions. Various free energy functionals, which are well-known in relation to simple materials, are generalized so that they apply to this fluid. In particular, expressions for the minimum free energy and a more recently AbstractWe consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they differ from the standard Graffi conditions. Various free energy functionals, which are well-known in relation to simple materials, are generalized so that they apply to this fluid. In particular, expressions for the minimum free energy and a more recently introduced explicit functional of G. Amendola

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Thermodynamics of a non-simple heat conductor with memory

Cited by 8 publications

References 22 publications

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

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

Entropy Principle and Recent Results in Non-Equilibrium Theories

Second gradient viscoelastic fluids: dissipation principle and free energies

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