Entropy-energy solutions for Thermo-Visco-Elastic systems with Mr\'oz-type inelastic behavior

Abstract

In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered problem, the temperature dependence appears in both the elastic and inelastic constitutive relations. For such a system, we introduce the concept of a weak entropy-energy solution, which satisfies the entropy equality instead of the internal energy equation. Although the model does not possess any mathematically favorable structural properties, such as Kelvin-Voigt type effects or simplifications eliminating temperature from the constitutive relations, we prove the global-in-time existence of weak entropy-energy solutions for large initial data.