Heat Conduction and Controlled Deformations in Incompressible Isotropic Elasticity

Author:

Dunwoody J.1,Ogden R. W.2

Affiliation:

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

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

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 ▿·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.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements;International Journal for Numerical Methods in Engineering;2018-05-22

2. Response of an Elastic Body whose Heat Conduction Is Pressure Dependent;Journal of Elasticity;2011-02-12

3. Implicit constitutive relations in thermoelasticity;International Journal of Non-Linear Mechanics;2011-01

4. Response of an Elastic Body whose Heat Conduction Is Pressure Dependent;Methods and Tastes in Modern Continuum Mechanics;2011

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