Thermo-visco-elasticity for Norton–Hoff-type models

Our research is directed to a quasi-static evolution of the thermo-visco-elastic model. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic. Moreover, our analysis captures the influence of the temperature on the visco-elastic properties of the body. The novelty of the paper is the consideration of the thermodynamically consistent model to describe this kind of phenomena related with a hardening rule of Norton–Hoff type. We provide the proof of existence of solutions to thermo-visco-elastic model in a simplified setting, namely the thermal expansion effects are neglected. Consequently, the coupling between the temperature and the displacement occurs only in the constitutive function for the evolution of the visco-elastic strain.