Thermo-visco-elasticity for Norton-Hoff-type models. (English) Zbl 1330.74043
Summary: 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.
MSC:
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74F05 | Thermal effects in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
thermodynamical consistency; visco-elasticity; thermal effects; Galerkin approximation; monotonicity method; renormalizationsReferences:
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