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

¹ Department of Applied Mathematics. Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain. ;
patricia.barral@usc.es
² Centro Universitario de la Defensa Zaragoza, Academia General Militar, Ctra. Huesca, s/n, 50090 Zaragoza, Spain.
tererua@unizar.es

Received: 2 October 2012
Revised: 22 May 2013

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.