The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez-Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will improve the former algorithms by means of a generalized duality method with variable parameters and we will present numerical results showing the applicability of the resultant algorithm to solidification processes. Furthermore, we will describe a numerical procedure to choose a constant parameter for the Bermúdez-Moreno algorithm which gives good results when it is applied to solidification processes.
Keywords: viscoplastic materials, duality methods, solidification process
@article{M2AN_2014__48_1_87_0,
author = {Barral, P. and Quintela, P. and S\'anchez, M. T.},
title = {A {Berm\'udez-Moreno} algorithm adapted to solve a viscoplastic problem in alloy solidification processes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {87--106},
year = {2014},
publisher = {EDP Sciences},
volume = {48},
number = {1},
doi = {10.1051/m2an/2013095},
mrnumber = {3177838},
zbl = {1286.74025},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2013095/}
}
TY - JOUR AU - Barral, P. AU - Quintela, P. AU - Sánchez, M. T. TI - A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 87 EP - 106 VL - 48 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2013095/ DO - 10.1051/m2an/2013095 LA - en ID - M2AN_2014__48_1_87_0 ER -
%0 Journal Article %A Barral, P. %A Quintela, P. %A Sánchez, M. T. %T A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 87-106 %V 48 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2013095/ %R 10.1051/m2an/2013095 %G en %F M2AN_2014__48_1_87_0
Barral, P.; Quintela, P.; Sánchez, M. T. A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 87-106. doi: 10.1051/m2an/2013095
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