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.
@article{M2AN_2011__45_3_477_0,
author = {Bartels, S\"oren and Roub\'\i \v cek, 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {477-504},
doi = {10.1051/m2an/2010063},
mrnumber = {2804647},
zbl = {1267.74037},
language = {en},
url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 477-504. doi : 10.1051/m2an/2010063. http://gdmltest.u-ga.fr/item/M2AN_2011__45_3_477_0/
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