Elasto-plastic contact problems with heat exchange

This paper deals with a dynamical model for the motion of a one-dimensional visco-elasto-plastic body in contact with an elasto-plastic obstacle and undergoing thermal expansion. The problem for the unknown displacement and temperature is rewritten in accordance with the formalism of hysteresis oper...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2015-04, Vol.22, p.551-567
Main Authors: Krejčí, Pavel, Petrov, Adrien
Format: Article
Language:English
Subjects:
Analysis of PDEs
Balancing
Contact
Dynamical systems
Elasto-plasticity
Heat equation
Hysteresis operators
Mathematical models
Mathematics
Nonlinearity
Obstacles
Operators
Thermal expansion
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Summary:This paper deals with a dynamical model for the motion of a one-dimensional visco-elasto-plastic body in contact with an elasto-plastic obstacle and undergoing thermal expansion. The problem for the unknown displacement and temperature is rewritten in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The system consists of the momentum balance and energy balance equations. The existence result for this thermodynamically consistent problem is obtained by using some a priori estimates established for the space discretized problem while the uniqueness result follows from the Lipschitz continuity of the nonlinearities.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2014.09.013