DD3IMP, 3D fully implicit finite element solver: implementation of CB2001 yield criterion


  • P. D. Barros
  • D. M. Neto
  • J. L. Alves
  • M. C. Oliveira
  • L. F. Menezes


DD3IMP, implicit time integration, sheet metal forming, elastoplasticity, orthotropy, CB2001 yield criterion


The strategies and algorithms adopted in the fully implicit FE solver DD3IMP to model the orthotropic behavior of metallic sheets, as well the procedure for parameters’ identification, are the main focus of this work; a special and detailed emphasis will be given to the numerical implementation of the Cazacu and Barlat (2001) yield criterion. The usage and application of the aforesaid solver and yield criterion will be exemplified with the deep drawing of a cylindrical cup, an example typically adopted to study the effect of the material’s orthotropy in forming operations. Two materials with distinct anisotropic behaviors are considered, namely: the AA5042 aluminum alloy and the AKDQ steel. The material parameters are identified from experimental data taking into account both flow stresses and r-values. The analysis of the results indicates that a good description of the anisotropy of both flow stresses and r-values are important to the overall accuracy of the predicted earing profile. However, either the global process history or the process parameters may influence the earing prediction, particularly the contact interactions with the flange during the forming process.


GANTAR, G., PEPELNJAK, T., KUZMAN, K., Optimization of sheet metal forming processes by the use of numerical simulations, J. Mater. Process. Technol., 130–131, pp. 54–59, 2002.

NOELS, L., STAINIER, L., PONTHOT, J-P., Combined implicit/explicit time-integration algorithms for the numerical simulation of sheet metal forming, J. Comput. Appl. Math., 168, pp. 331–339, 2004.

YANG, D.Y., JUNG, D.W., SONG, I.S., YOO, D.J., LEE, J.H., Comparative investigation into implicit, explicit, and iterative implicit/explicit schemes for the simulation of sheet-metal forming processes, J. Mater. Process. Technol., 50, pp. 39–53, 1995.

TEKKAYA, A.E., MARTINS, P.A.F., Accuracy, reliability and validity of finite element analysis in metal forming: a user’s perspective, Engineering Computations, 26, 8, pp. 1026–1055, 2009.

SAFAEI, M., Constitutive modelling of anisotropic sheet metals based on a non-associated flow rule, PhD Thesis, Faculty of Engineering and Architecture, Ghent University, Belgium, 2013.

NETO, D.M., OLIVEIRA, M.C., ALVES, J.L., MENEZES, L.F., Influence of the plastic anisotropy modelling in the reverse deep drawing process simulation, Mater Des, 60, pp. 368– 379, 2014.

CAZACU, O., BARLAT, F., Generalization of Drucker’s Yield Criterion to Orthotropy, Math. Mech. Solids., 6, 6, pp. 613–630, 2001.

MENEZES, L.F., TEODOSIU, C., Three-dimensional numerical simulation of the deep-drawing process using solid finite elements, J. Mater. Process. Technol., 97, pp. 100–106, 2000.

OLIVEIRA, M.C., ALVES, J.L., MENEZES, L.F., Algorithms and Strategies for Treatment of Large Deformation Frictional Contact in the Numerical Simulation of Deep Drawing Process, Arch. Comput. Methods. Eng., 15, pp. 113–162, 2008.

ALART, P., CURNIER, A., A mixed formulation for frictional contact problems prone to Newton like solution methods, Comput. Methods. Appl. Mech. Eng., 92, 3, pp. 353–375, 1991.