A thermo-mechanically coupled nonlinear viscoelastic-viscoplastic cyclic constitutive model for polymeric materials

Thermo-mechanically coupled cyclic deformations often occur in polymeric components subjected to a cyclic loading. In this work, a framework of irreversible thermodynamics at small deformation is presented at first to model the thermo-mechanically coupled cyclic deformation of polymeric materials. Two inelastic mechanisms, i.e., viscoelasticity and viscoplasticity are considered, simultaneously. The thermodynamic state of the material is defined by certain state variables and the Gibbs free energy is decomposed into four parts, i.e., the instantaneous elastic, the viscoelastic, the viscoplastic and the ones related to temperature. The driving forces of the strain-like internal variables related to the viscoelasticity and viscoplasticity are deduced from the constructed Gibbs free energy and Clausius's dissipative inequality. The internal heat production and the spatio-temporal evolution equation of temperature are obtained by the first law of thermodynamics. Then, based on the experimental observations on the cyclic deformation of ultra-high molecular weight polyethylene (UHMWPE), a specific constitutive model is proposed by adopting some simplifications. Finally, the capability of the proposed model is verified by comparing the predicted results with the corresponding experimental ones of the UHMWPE. It is seen that the temperature- and rate-dependent cyclic deformation and the evolution of temperature can be reasonably predicted by the proposed model.