An internal-variable theory of thermo-viscoelastic constitutive relations at finite strain

Based on the nonequilibrium thermodynamic theory, a new thermo-viscoelastic relation at finite strain is proposed. Under the assumption that the speci fic heat at a fixed strain and fixed internal variables can be regarded as a constant, a new expression for the free energy which decouples the mechan ical and the thermal effects is derived. Through an analysis of the mesosco pic deformation mechanism of solid polymers, a set of internal variables is introduced, and an internal-variable constitutive theory in thermo-viscoel asticity at finite strain is formulated. An explicit expression of a thermo viscoelastic constitutive relation is obtained for solid polymers in the ca se where their molecular network has a randomly oriented distribution funct ion at reference configuration. Moreover, the relationship between the rela xation time and the temperature is also discussed. The viscoelastic constit utive theory proposed in reference is only a linear approximation of the pr esent theory.