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Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion*

Published online by Cambridge University Press:  11 October 2010

Sören Bartels  and
Tomáš Roubíček
Sören Bartels
Affiliation:
Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstraße 6, 53115 Bonn, Germany. bartels@ins.uni.bonn.de
Tomáš Roubíček
Affiliation:
Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00 Praha 8, Czech Republic.
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Abstract

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive limit passage. Computational 3D simulations illustrate an implementation of the method as well as physical effects of residual stresses substantially depending on rate of heat treatment.

Keywords

Thermodynamics of plasticityKelvin-Voigt rheologyhardeningthermal expansionadiabatic effectsfinite element methodimplicit time discretizationconvergence
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 3 , May 2011 , pp. 477 - 504
Copyright
© EDP Sciences, SMAI, 2010

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