Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 1, January 2005, Pages 173 - 178

Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity

Authors
Sandra Carillo
Corresponding Author
Sandra Carillo
Available Online 1 January 2005.
DOI
10.2991/jnmp.2005.12.s1.14How to use a DOI?
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
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - Supplement 1
Pages
173 - 178
Publication Date
2005/01/01
ISBN
91-974824-3-9
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2005.12.s1.14How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Sandra Carillo
PY  - 2005
DA  - 2005/01/01
TI  - Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity
JO  - Journal of Nonlinear Mathematical Physics
SP  - 173
EP  - 178
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.14
DO  - 10.2991/jnmp.2005.12.s1.14
ID  - Carillo2005
ER  -