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

2014/04/07 by Gwiazda, Piotr, Klawe, Filip Z., Świerczewska-Gwiazda, Agnieszka
#35Q74 #74C10 #74F05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.1671

Abstract

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 complete 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.

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