A new viscoelastic constitutive model for continuous media at finite thermomechanical changes

This paper is concerned with the continuum formulation of a fully coupled thermomechanical constitutive model for highly deformable bodies with viscous dissipation. The threedimensional material law is applicable to the thermomechanical characterization of elastomeric (high-polymeric) solids in the finite strain domain under varying temperature. The description is based on the concept of internal state variables and rational thermodynamics. The main goal of the presentation is to develop consistent constitutive equations for the stress, entropy and independent internal variables such that the second law of thermodynamics, in the form of the Clausius-Duhem inequality, issatisfied. Motivated by the significant difference in bulk and shear response of elastomers, the model employs a local decomposition of the deformation into a dilatational and an isochoric part. The framework of nonlinear thermoviscoelasticity presented herein is formulated entirely in the reference configuration and provides a sound continuum basis for approximation techniques such as the Finite-Element method.