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On one mathematical model of creep in superalloys. (English) Zbl 1042.74511
Summary: The paper deals with modelling of creep in superalloys. The modelled area \(\Omega \subset {\mathbb R}^3\) consists of subdomains \(\Omega _1,\dots ,\Omega _n\) representing mutually separated elastic particles and their complement \(\Omega _0\) representing creeping matrix. The model consists of equations of motion, constitutive relations for viscoelastic material, compatibility conditions on the interface of domains and equations for evolution of the dislocation density. In the matrix the creep is active in a finite number of slip systems.
In the paper precise weak formulation of this complicated evolution system of PDE is introduced and existence of the solution is proved by means of the Rothe method.
Reviewer: J. Franců (Brno)

MSC:
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
74H99 Dynamical problems in solid mechanics
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