Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy

Citation
Am. Maniatty et al., Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy, COMPUT METH, 190(35-36), 2001, pp. 4609-4625
Citations number
19
Categorie Soggetti
Mechanical Engineering
Journal title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN journal
00457825 → ACNP
Volume
190
Issue
35-36
Year of publication
2001
Pages
4609 - 4625
Database
ISI
SICI code
0045-7825(2001)190:35-36<4609:SFEMFV>2.0.ZU;2-Z
Abstract
This paper presents a stabilized finite element formulation for steady-stat e viscoplastic Row and a simple strategy for solving the resulting non-line ar equations with a Newton-Raphson algorithm. An Eulerian stabilized finite element formulation is presented, where mesh dependent terms are added ele ment-wise to enhance the stability of the mixed finite element formulation. A local reconstruction method is used for computing derivatives of the str ess field needed when higher order elements are used. Linearization of the weak form is derived to enable a Newton-Raphson solution procedure of the r esulting non-linear equations. In order to get convergence in the Newton-Ra phson algorithm, a trial solution is needed which is within the radius of c onvergence. An effective strategy for progressively moving inside the radiu s of convergence for highly non-linear viscoplastic constitutive equations, typical of metals, is presented. Numerical experiments using the stabiliza tion method with both linear and quadratic shape functions for the velocity and pressure fields in viscoplastic flow problems show that the stabilized method and the progressive convergence strategy are effective in non-linea r steady forming problems. Finally, conclusions are inferred and extensions of this work are discussed. (C) 2001 Elsevier Science B.V. All rights rese rved.