Ceramics-Silikáty 49 (4) 242-251 (2005)

THE LINEAR THEORY OF THERMOELASTICITY FROM THE VIEWPOINT OF RATIONAL THERMOMECHANICS

W. Pabst

Linear thermoelasticity is summarized for materials scientists and engineers from the viewpoint of exact theory (rational thermomechanics). It is developd in referential formulation, using the first Piola-Kirchhoff stress tensor, the referential heat flux, the free energy and the entropy as the material responses for which constitutive equations are given. The deformation gradient, the temperature and the referential temperature gradient are used as independent variables (simple thermoelastic materials). Linear approximations of the series expansions about a natural reference state and thermal equilibrium are invoked to define the elasticity tensor, the stress-temperature tensor, the thermal expansion tensor, the latent heat tensors, the heat conductivity tensor and the specific heats for anisotropic solids. Constitutive equations and linear thermoelastic properties of isotropic solids and fluids are derived as special cases

Keywords: Linear thermoelasticity, Thermal expansion tensor, Heat conductivity tensor, Specific heats, Isothermal and adiabatic elasticity tensors