Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity
- 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/).
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 -