PROC
Nonlinear semigroup methods in problems with hysteresis
Jana Kopfová
Results from a nonlinear semigroup theory are applied to get ex- istence and uniqueness for PDEs with hysteresis. The hysteresis nonlinearity considered is of the generalized play operator type, but can be easily extended to a generalized Prandtl-Ishlinskii operator of play type, both possibly discontinuous.
keywords: Hysteresis nonlinear semigroups.
DCDS-S
Thermodynamical consistency - a mystery or?
Jana Kopfová
The goal of this note is to discuss the basic thermodynamical principles and show how they need to be considered in the process of developing new mathematical models. We give numerous examples: linear elasticity with constant or non-constant temperature, we discuss classical hysteresis models as the play operator, the Preisach operator as well as new models introduced in the last years - the temperature dependent Preisach model, models of magnetostriction and models of an oscillating beam with fatigue.
keywords: hysteresis Thermodynamical consistency fatigue Preisach model. magnetostriction
DCDS
A new phase field model for material fatigue in an oscillating elastoplastic beam
Michela Eleuteri Jana Kopfová Pavel Krejčí
We pursue the study of fatigue accumulation in an oscillating elastoplastic beam under the additional hypothesis that the material can partially recover by the effect of melting. The full system consists of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics. The main result consists in proving the existence and uniqueness of a strong solution.
keywords: Prandtl-Ishlinskii operator material fatigue thermo-elasto-plasticity Elastoplastic beam phase transition.
DCDS-B
Fatigue accumulation in a thermo-visco-elastoplastic plate
Michela Eleuteri Jana Kopfová Pavel Krejčí
We consider a thermodynamic model for fatigue accumulation in an oscillating elastoplastic Kirchhoff plate based on the hypothesis that the fatigue accumulation rate is proportional to the plastic part of the dissipation rate. For the full model with periodic boundary conditions we prove existence of a solution in the whole time interval.
keywords: Prandtl-Ishlinskii operator material fatigue. Elastoplastic plate
CPAA
Non-isothermal cyclic fatigue in an oscillating elastoplastic beam
Michela Eleuteri Jana Kopfová Pavel Krejčí
We propose a temperature dependent model for fatigue accumulation in an oscillating elastoplastic beam. The full system consists of the momentum and energy balance equations, and an evolution equation for the fatigue rate. The main modeling hypothesis is that the fatigue accumulation rate is proportional to the dissipation rate. In nontrivial cases, the process develops a thermal singularity in finite time. The main result consists in proving the existence and uniqueness of a strong solution in a time interval depending on the size of the data.
keywords: blow-up. Elastoplastic beam material fatigue thermo-elasto-plasticity Prandtl-Ishlinskii operator

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