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.
Mots-clés : thermodynamics of plasticity, Kelvin-Voigt rheology, hardening, thermal expansion, adiabatic effects, finite element method, implicit time discretization, convergence
@article{M2AN_2011__45_3_477_0,
author = {Bartels, S\"oren and Roub{\'\i}\v{c}ek, Tom\'a\v{s}},
title = {Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {477--504},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
doi = {10.1051/m2an/2010063},
mrnumber = {2804647},
zbl = {1267.74037},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010063/}
}
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 PY - 2011 SP - 477 EP - 504 VL - 45 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010063/ DO - 10.1051/m2an/2010063 LA - en ID - M2AN_2011__45_3_477_0 ER -
%0 Journal Article %A Bartels, Sören %A Roubíček, Tomáš %T Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 477-504 %V 45 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010063/ %R 10.1051/m2an/2010063 %G en %F M2AN_2011__45_3_477_0
Bartels, Sören; Roubíček, Tomáš. Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 3, pp. 477-504. doi : 10.1051/m2an/2010063. http://www.numdam.org/articles/10.1051/m2an/2010063/
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