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

Sören Bartels; Tomáš Roubíček

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 3, page 477-504
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bartels, Sören, and Roubíček, Tomáš. "Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.3 (2011): 477-504. <http://eudml.org/doc/273101>.

@article{Bartels2011,
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.},
author = {Bartels, Sören, Roubíček, Tomáš},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thermodynamics of plasticity; Kelvin-Voigt rheology; hardening; thermal expansion; adiabatic effects; finite element method; implicit time discretization; convergence},
language = {eng},
number = {3},
pages = {477-504},
publisher = {EDP-Sciences},
title = {Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion},
url = {http://eudml.org/doc/273101},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Bartels, Sören
AU - Roubíček, Tomáš
TI - Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 3
SP - 477
EP - 504
AB - 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.
LA - eng
KW - thermodynamics of plasticity; Kelvin-Voigt rheology; hardening; thermal expansion; adiabatic effects; finite element method; implicit time discretization; convergence
UR - http://eudml.org/doc/273101
ER -

References

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