A thermo-viscoelastic constitutive model for compressible amorphous polymers

We propose a compressible thermo-viscoelastic constitutive model at finite deformation for amorphous polymers. Firstly, the compressible hyperelastic deformation energy is extended to include thermal effect. Secondly, in order to describe the viscous property of the materials, internal variables are introduced into the above thermo-hyperelastic constitutive relation. As the Maxwell model is equivalent to the transient network model under certain condition, the rationality of introducing the internal variables for a general deformation mode is proved. The model only contains a few material parameters, just necessary for a complicated thermal-mechanical coupling system. Besides, this model provides an explanation for the deformation energy function from the microscopic mechanism. Based on this model, the influences of the loading rate, compressibility and the thermal expansion coefficient on the coupled thermo-mechanical behavior of polymers are discussed.