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

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 specific 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 mechanical and the thermal effects is derived. Through an analysis of the mesoscopic deformation mechanism of solid polymers, a set of internal variables is introduced, and an internal-variable constitutive theory in thermo-viscoelasticity at finite strain is formulated. An explicit expression of a thermoviscoelastic constitutive relation is obtained for solid polymers in the case where their molecular network has a randomly oriented distribution function at reference configuration. Moreover, the relationship between the relaxation time and the temperature is also discussed. The viscoelastic constitutive theory proposed in reference is only a linear approximation of the present theory.