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A Bermúdez–Moreno algorithm adapted to solve a viscoplasticproblem in alloy solidification processes

Published online by Cambridge University Press:  15 November 2013

P. Barral ,
P. Quintela  and
M. T. Sánchez
P. Barral
Affiliation:
Department of Applied Mathematics. Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain.. patricia.barral@usc.es ; peregrina.quintela@usc.es ;
P. Quintela
Affiliation:
Department of Applied Mathematics. Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain.. patricia.barral@usc.es ; peregrina.quintela@usc.es ;
M. T. Sánchez
Affiliation:
Centro Universitario de la Defensa Zaragoza, Academia General Militar, Ctra. Huesca, s/n, 50090 Zaragoza, Spain.; tererua@unizar.es
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Abstract

The aim of this work is to present a computationally efficient algorithm to simulate thedeformations suffered by a viscoplastic body in a solidification process. This type ofproblems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. Inour previous papers, this difficulty has been solved by means of a duality method, knownas Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed pointalgorithm or a Newton method. In this paper, we will improve the former algorithms bymeans of a generalized duality method with variable parameters and we will presentnumerical results showing the applicability of the resultant algorithm to solidificationprocesses. Furthermore, we will describe a numerical procedure to choose a constantparameter for the Bermúdez–Moreno algorithm which gives good results when it is applied tosolidification processes.

Keywords

Viscoplastic materialsduality methodssolidification process

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 87 - 106
Copyright
© EDP Sciences, SMAI 2013

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