The sheet metal forming process is used in almost all kinds of industrial domains. It is controlled by an enormous amount of technological parameters, reason why the numerical simulation became a fundamental tool for the process analysis. To obtain accurate solutions, the mechanical models implemented in the simulation codes should use reliable descriptions of the plastic behaviour of the deformed materials. The most widely used constitutive model is the classical Hill48 yield criterion, to characterize the anisotropy, with a power law that describe the hardening behaviour. However, during a stamping operation, the stress condition is not always uniaxial and the strain paths are not monotonic even in single stage processes. Under complex strain-path changes a simple power law does not provide an accurate simulation of the material behaviour. Thus, more sophisticated models, involving non-linear kinematic hardening and internal state variables, are expected to allow an improvement in the simulation of the deep drawing forming process. The present paper presents a short review of a few advanced constitutive models. The five selected models were previously implemented in the finite element code DD3IMP. Two are classical pure isotropic hardening models described by a power law (Swift) or a Voce type saturation equation. Those two models were also combined with a non-linear (Lemaître and Chaboche) kinematic hardening rule. The final one is the Teodosiu microstructural hardening model. Comparative analyses of numerical results, obtained with these constitutive models, are presented. The simulations consist on the stamping of a curved rail developed in the project 3DS. Introduction The optimisation of the deep drawing process parameters is often made using numeric tools since it allows evaluating the stamping force evolution, springback, residual stresses, etc. To perform accurately these tasks the material models should be able to predict the material behaviour under severe strain path changes, such as modification of the elastoplastic behaviour when passing through drawbeads, localized deformation and premature rupture after orthogonal strain-path changes, and modification of the springback behaviour Five constitutive models were compared in this study in order to evaluate their influence in the simulation results. The simulations were performed with the DD3IMP finite element code; a 3-D elastoplastic finite element code following a fully implicit time integration scheme [1-3]. The Coulombs law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton-Raphson type is used to solve the non-linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The code uses solid finite elements to describe the deformable sheet and Bézier surfaces to describe the rigid tools. Materials Science Forum Online: 2004-05-15 ISSN: 1662-9752, Vols. 455-456, pp 717-722 doi:10.4028/www.scientific.net/MSF.455-456.717 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-11/03/20,15:41:32) 718 Title of Publication (to be inserted by the publisher) The deep drawing problem selected for this analysis is a curved rail, develop under the 3DS project [4], specially conceived to emphasize 3-D springback. Constitutive Models To model the plastic behaviour it is necessary to define the flow rule, the yield stress evolution and the hardening behaviour. In this work, we assume that the plastic strain rate, p D , is given by the associated flow rule: ( ) X M D = = : p & & , (1) where & is the plastic multiplier, is the yield function, is the stress tensor, is the deviator of the stress tensor, M is a fourth-order tensor characterizing the anisotropy and X is the back stress tensor. The anisotropic model used in this work is the classical Hill48 yield criteria [5]. The equivalent stress is obtained as: ( ) ( ). X : M : X = (2) The equivalent plastic strain p can be defined, manipulating Eq. 1, as: ( ) t d t d t