Generalized Hypo-Elasticity with Thermal Influence : I. Constitutive Equations

Abstract

The constitutive equations of the generalized hypo-elastic materials with thermal influence are derived and defined from those of the isotropic thermo-elastic material with invertible stress relation. In order to remedy the infinite magnitude of propagation of thermal disturbance the deformation gradient, the temperature and the summed history of temperature gradient are adopted as independent state variables. Then the constitutive equations are defined from the heuristic basis. The restriction by the Clausius-Duhem inequality is discussed and the coefficients of constitutive equations are represented by the theorem of isotropic functions.