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
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.