Thermo-visco-elasticity for Norton-Hoff-type models with homogeneous thermal expansion

The novelty of this paper is to take into account the thermal expansion of material. We are proposing linearization of the model for homogeneous thermal expansion, which preserves symmetry of system and therefore total energy is conserved. Linearization of material's thermal expansion is performed in definition of Cauchy stress tensor and in heat equation. In previous studies, it was done in different way. Consideration of such linearization leads to system where the coupling between temperature and displacement occurs in two places, i.e. in the constitutive function for the evolution of visco-elastic strain and in the additional term in the heat equation, in comparison to models without thermal expansion. The second coupling was not considered previously. For such system of equations we prove the existence of solutions. Moreover, we obtain existence of displacement's time derivative, which has not been done previously.