On rigid linear heat conductors with memory

Fabrizio, Mauro; Gentili, G.; Reynolds, David W.

doi:10.1016/s0020-7225(97)00123-7

Cited by 63 publications

(82 citation statements)

References 16 publications

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“…In particular, the approach presented by Fabrizio, Gentili and Reynolds in [11], and, subsequently, in [2] is adopted. Accordingly, the key notions comprised in [2] are briefly reviewed.…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

“…The heat flux q ∈ R 3 , when the heat flux relaxation function denoted by k(x, t), is assumed to satisfy the constitutive equation 2) which shows that the heat flux q depends on the time variable not only via the present time t, but also via its past history. In addition, according to [11] and [2], the rigid heat conductor is understood to be an isotropic material, and, hence, focussing the attention on a generic element of the conductor, no dependence on the position in the conductor is considered. Then, the energy e, the heat flux q, the temperature θ and, consequently, all the other quantities are represented by functions of the time variable alone.…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

“…The thermodynamical state of the conductor is characterized when, according to [11], [22] and [2], the thermodynamic state function σ : R → R×R 3 which associates t −→ σ(t) ≡ θ(t),ḡ t is given; that is, when the temperature and the integrated history of the temperature-gradient,ḡ t which belong to a suitable Hilbert space, are assigned. In addition, physically admissible thermodynamical phenomena, namely associated to finite heat flux, are those ones which belong to the following vectorial space…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

“…The definitions of process and of the set of admissible states, given in [11], see also [2], are here only briefly recalled. An integrable function P :…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

“…The opening Section 2 is devoted to briefly recall the model, according to [11], of a rigid heat conductor with memory. Specifically, the thermodynamic state function is defined and, subsequently, the meaning of what termed process, process prolongation and some related quantities, are exploited.…”

Section: Introductionmentioning

confidence: 99%

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Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity

Carillo¹

2005

JNMP

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Materials with memory are here considered. The introduction of the dependence on time not only via the present, but also, via the past time represents a way, alternative to the introduction of possible non linearities, when the physical problem under investigation cannot be suitably described by any linear model. Specifically, the two different models of a rigid heat conductor, on one side, and of a viscoelastic body, on the other one, are analyzed. In them both, to evaluate the quantities of physical interest a key role is played by the past history of the material and, accordingly, the behaviour of such materials is characterized by suitable constitutive equations where Volterra type kernels appear. Specifically, in the heat conduction problem, the heat flux is related to the history of the temperature-gradient while, in isothermal viscoelasticity, the stress tensor is related to the strain history. Then, the notion of equivalence is considered to single out and associate together all those different thermal histories, or, in turn, strain histories, which produce the same work. The corresponding explicit expressions of the minimum free energy are compared.

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“…In particular, the approach presented by Fabrizio, Gentili and Reynolds in [11], and, subsequently, in [2] is adopted. Accordingly, the key notions comprised in [2] are briefly reviewed.…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

“…The definitions of process and of the set of admissible states, given in [11], see also [2], are here only briefly recalled. An integrable function P :…”

Section: Heat Conduction In a Rigid Solidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations