Atlantis Press Paper Details: Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity

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, alterntive 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 viscoelaticity, 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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title:		Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity
publication:		JNMP
volume-issue:		12 - Supplement 1
pages:		173 - 178
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.s1.14 (how to use a DOI)
author(s):		Sandra CARILLO
publication date:		January 2005
abstract:		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, alterntive 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 viscoelaticity, 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.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		12s1_14.pdf (188 K)