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Mathematics and Mechanics of Solids
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Heat Conduction and Controlled Deformations in Incompressible Isotropic Elasticity

J. Dunwoody

School of Mathematics and Physics, The Queen's University of Belfast, Belfast BT7 1NN, UK

R. W. Ogden

Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK

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 {triangledown}·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.

Key Words: nonlinear thermoelasticity • isotropic thermoelasticity • finite deformations • controlable deformations • heat conduction

Mathematics and Mechanics of Solids, Vol. 10, No. 5, 487-502 (2005)
DOI: 10.1177/1081286505036416
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