Termo-lepko-elastyczny model Mroza

The subject of our research is a quasi-static evolution of the thermo-visco-elastic model. In the considered model the mechanical deformation is coupled with a heat equation. Mechanical deformation consists of two types of deformation: elastic and inelastic. Inelastic deformation is consistent with the Mróz model. There exists a coupling between the Cauchy stress tensor and the temperature in the constitutive function for evolution of inelastic deformation.

The novelty of the paper is the consideration of the thermodynamically consistent model to describe this kind of phenomena related with Mróz hardening role. We provide the proof regarding solutions' existence of thermo-visco-elastic model in simpler form - we omit the thermal expansion e ects, therefore, the coupling between the temperature and the displacement occurs only in the constitutive function for evolution of the visco-elastic deformation G(·, ·).