# A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes

• Volume: 48, Issue: 1, page 87-106
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Barral, P., Quintela, P., and Sánchez, M. T.. "A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.1 (2014): 87-106. <http://eudml.org/doc/273349>.

@article{Barral2014,
abstract = {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.},
author = {Barral, P., Quintela, P., Sánchez, M. T.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {viscoplastic materials; duality methods; solidification process},
language = {eng},
number = {1},
pages = {87-106},
publisher = {EDP-Sciences},
title = {A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes},
url = {http://eudml.org/doc/273349},
volume = {48},
year = {2014},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 1
SP - 87
EP - 106
AB - 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.
LA - eng
KW - viscoplastic materials; duality methods; solidification process
UR - http://eudml.org/doc/273349
ER -

## References

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