Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-16T00:24:17.802Z Has data issue: false hasContentIssue false
  • English
  • Français

A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem 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
Get access

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.

Keywords

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arregui, I., Cendán, J.J., Parés, C. and Vázquez, C., Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices. ESAIM: M2AN 42 (2008) 645–665. Google Scholar
Barral, P., Bermúdez, A., Muñiz, M.C., Otero, M.V., Quintela, P. and Salgado, P., Numerical simulation of some problems related to aluminium casting. J. Mater. Process. Technol. 142 (2003) 383–399. Google Scholar
Barral, P., Moreno, C., Quintela, P. and Sánchez, M.T., A numerical algorithm for a Signorini problem associated with Maxwell-Norton materials by using generalized Newton’s methods. Comput. Methods Appl. Mech. Engrg. 195 (2006) 880–904. Google Scholar
Barral, P. and Quintela, P., A numerical algorithm for prediction of thermomechanical deformation during the casting of aluminium alloy ingots. Finite Elem. Anal. Des. 34 (2000) 125–143. Google Scholar
Barral, P. and Quintela, P., Asymptotic justification of the treatment of a metallostatic pressure type boundary condition in an aluminium casting. Math. Models Methods Appl. Sci. 11 (2001) 951–977. Google Scholar
Bermúdez, A. and Moreno, C., Duality methods for solving variational inequalities. Comput. Math. Appl. 7 (1981) 43–58. Google Scholar
Bermúdez, A. and Otero, M.V., Numerical solution of a three-dimensional solidification problem in aluminium casting. Finite Elem. Anal. Des. 40 (2004) 1885–1906. Google Scholar
J.M. Drezet and M. Plata, Thermomechanical effects during direct chill and electromagnetic casting of aluminum alloys. Part I: Experimental investigation. Light Metals (1995) 931–940.
J.M. Drezet, M. Rappaz and Y. Krahenbuhl, Thermomechanical effects during direct chill and electromagnetic casting of aluminum alloys. Part II: numerical simulation. Light Metals (1995) 941–950.
T.S. El-Raghy, H.A. El-Demerdash, H.A. Ahmed and A.M. El-Sheikh, Modelling of the transient and steady state periods during aluminium dc casting. Light Models (1995) 925–929.
M.C. Flemings, Solidification processing. In McGraw-Hill Series in Materials Science and Engineering. McGraw-Hill, New York (1974).
Friaâ, A., Le matériau de Norton-Hoff généralisé et ses applications en analyse limite. C. R. Acad. Sci. Paris Sér. A-B 286 (1978) A953–A956. Google Scholar
Gallardo, J.M., Parés, C. and Castro, M., A generalized duality method for solving variational inequalities. Applications to some nonlinear Dirichlet problems. Numer. Math. 100 (2005) 259–291. Google Scholar
J. Lemaitre and J.L. Chaboche, Mécanique des matériaux solides. Dunod, Paris (1988).
S. Mariaux, M. Rappaz, Y. Krahenbuhl and M. Plata, Modelling of Thermomechanical Effects During the Start-Up Phase of the Electromagnetic Casting Process. Advances in Production and Fabrication of Light Metals and Metal Matrix Composites (1992) 175–187.
Naya, M.C. and Quintela, P., Modelling of materials with long memory. Int. J. Solids Struct. 45 (2008) 6133–6156. Google Scholar
Parés, C., Castro, M. and Macías, J., On the convergence of the Bermúdez-Moreno algorithm with constant parameters. Numer. Math. 92 (2002) 113–128. Google Scholar
W. Schneider, E.K. Jensen and B. Carrupt, Development of a new starting block shape for the dc casting of sheet ingots. Part I: Experimental results. Light Metals (1995) 961–967.
Wong, W.A. and Jonas, J.J., Aluminum extrusion as a thermally activated process. Trans. Metall. Soc. AIME 242 (1968) 2271–2280. Google Scholar