Analyticity of solutions to thermo‐elastic‐plastic flow problem with microtemperatures

Abstract

In this paper, we study some qualitative and numerical properties of new equations including the coupled effects of thermal elastic-plastic theory with microtemperatures. We establish the necessary and sufficient conditions to guarantee that the model dissipates energy. The one-dimensional case, which corresponds to isotropic hardening problem, is chosen in order to present some qualitative and numerical properties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the one-dimensional problem corresponding to plastic flow. Then, we show that the associated C0−semigroup is not analytical in general, except for a special case. The exponential stability of the solutions is kept in all cases. Finally, a numerical tool, based on the finite element method, is developed to validate the proposed model and to show its capability. Particular attention is paid to the consideration of the elastoplastic behavior in the development of this tool.

Decay in full von Kármán beam with temperature and microtemperatures effects

“…( 11) of [23]), in the theory of thermo-elastic-plasticity flow with microtemperatures (see Eq. (4.1) of [3]) and in others (see e.g. [23][24][25]).…”