Heat conduction and controlled deformations in incompressible isotropic elasticity

Dunwoody, J. and Ogden, R.W. (2005) Heat conduction and controlled deformations in incompressible isotropic elasticity. Mathematics and Mechanics of Solids, 10(5), pp. 487-502. (doi:10.1177/1081286505036416)

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Publisher's URL: http://dx.doi.org/10.1177/1081286505036416

Abstract

For incompressible isotropic elastic heat conducting solids we examine the classes of universal deformations that are controllable under homothermal conditions and, in respect of a general law of heat conduction, determine the members of these classes that can support non-homothermal temperature fields. It is shown, in particular, that in some cases the values of the components of the (Cauchy) stress tensor T necessary for the satisfaction of the equilibrium equation del center dot T = 0 in the homothermal. problem are retained in the corresponding non-homothermal problem to within an additive constant. These observations have implications for the design of experiments in which a material is subject to a temperature gradient since it is of value to know in advance that a specific deformation can be controlled in the presence of a suitable temperature gradient. The temperature may then be obtained as the solution of the steady state heat equation.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Dunwoody, J., and Ogden, R.W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematics and Mechanics of Solids
ISSN:1081-2865
ISSN (Online):1741-3028

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