Skip to main content
Log in

A three field element via Augmented Lagrangian for modelling bulk metal forming processes

  • Originals
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A new 2D quadrilateral element is developed for the modelling of 2D incompressible rigid/viscoplastic problems: the QMITC-3F. The element formulation is based on the interpolation of three fields: velocities, strain rates and pressures. The incompressibility constraint is enforced using an Augmented Lagrangian technique. The new element is used in conjunction with the flow formulation and the pseudo-concentrations technique for modelling bulk metal forming processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Argyris, J. H.; Doltsinis, J. St.; Knudson, W. C.; Szimmot, J.; Willam, K. J.; Wüstenberg, H. 1980: Eulerian and Lagrangian techniques for elastic and inelastic large deformation processes. In: J. T.Oden (Ed.), Computational Methods in Nonlinear Mechanics, 13–66, North-Holland, Amsterdam

    Google Scholar 

  • Backofen, W. A. 1972: Deformation Processing, Addison-Wesley, Reading, MA

    Google Scholar 

  • Bathe, K. J. 1982: Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Brooks, A. N.; Hughes, T. J. R. 1982: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp. Meth. Appl. Mech. Engrg. 32: 199–259

    Google Scholar 

  • Chen, C. C.; Kobayashi, S. 1979: Rigid-plastic finite element analysis of plastic deformation in metal-forming processes. Technical Report AFML-TR-79-4105, USA Wright-Patterson Air Force Base

  • Codina, R. 1993a: An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations. Comp. Meth. Appl. Mech. Engrg. 110: 237–262

    Google Scholar 

  • Codina, R. 1993b. A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation. Comp. Meth. Appl. Mech. Engrg. 110: 325–342

    Google Scholar 

  • Dvorkin, E. N.; Assanelli, A. P. 1990: Elasto-plastic analysis using a quadrilateral 2D element based on mixed interpolation of tensorial components. In: Owen, D. R. J. et al. (Eds.), Proc. Second International Conference on Computational Plasticity, 263–283, Pineridge Press, Swansea

    Google Scholar 

  • Dvorkin, E. N.; Canga, M. E. 1993: Incompressible viscoplastic flow analysis using a quadrilateral 2D element based on mixed interpolation of tensorial components. Commun. Num. Meth. Eng. 9: 157–164

    Google Scholar 

  • Dvorkin, E. N.; Pantuso, D.; Repetto, E. A. 1994: A finite element formulation for finite strain elasto-plastic analysis based on mixed interpolation of tensorial components. Comp. Meth. Appl. Mech. Engrg. 114: 35–54

    Google Scholar 

  • Dvorkin, E. N.; Petöcz, E. G. 1992: On the modelling of 2D metal forming processes using the flow formulation and the pseudo-concentrations technique. In: Owen, D. R. J. et al. (Eds.), Proc. Third Int. Conf. on Computational Plasticity, 1037–1052, Pineridge Press, Swansea

    Google Scholar 

  • Dvorkin, E. N.: Petöcz, E. G. 1993: An effective technique for modelling 2D metal forming processes using an Eulerian formulation. Eng. Comput. 10: 323–336

    Google Scholar 

  • Dvorkin, E. N.; Vassolo, S. I. 1989: A quadrilateral 2D finite element based on mixed interpolation of tensorial components. Eng. Comput 6: 217–224

    Google Scholar 

  • Felippa, C. A. 1978: Iterative procedures for improving penalty function solutions of algebraic systems. Int. J. Num. Meth. Engrg., 12: 821–836

    Google Scholar 

  • Fortin, M.; Fortin, A. 1985: A generalization of Uzawa's algorithm for the solution of the Navier-Stokes equations. Commun. Num. Meth. Eng. 1: 205–208

    Google Scholar 

  • Hughes, T. J. R.; Brooks, A. 1982: A theorical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. In: Gallagher, R. H. et al. (Eds.), Finite Elements in Fluids, Vol. 4, 47–65, John Wiley & Sons Ltd, New York

    Google Scholar 

  • Kobayashi, S.; Oh, S.; Altan, T. 1989: Metal forming and the finite-element method, Oxford University Press, New York

    Google Scholar 

  • Li, G.; Kobayashi, S. 1982: Rigid-plastic finite-element analysis of plane strain rolling. J. of Engineering for Industry., 104: 55–63

    Google Scholar 

  • Luenberger, D. G. 1984: Linear and Nonlinear Programming, Addison-Wesley, Reading, MA

    Google Scholar 

  • Malvern, L. E. 1969: Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  • Perzyna, P. 1966: Fundamental problems in viscoplasticity. Advances in Applied Mechanics., 9, Academic Press, New York

    Google Scholar 

  • Simo, J. C.; Laursen, T. A. 1992: An Augmented Lagrangian treatment of contact problems involving friction. Comp. & Struct. 42: 97–116

    Google Scholar 

  • Thompson, E. 1986: Use of the pseudo-concentrations to follow creeping viscous flows during transient analysis. Int. J. Num. Meth. Fluids 6: 749–761

    Google Scholar 

  • Thompson, E.; Smelser, R. E. 1988: Transient analysis of forging operations by the pseudo-concentrations method. Int. J. Num. Meth. Engrg. 25: 177–189

    Google Scholar 

  • Washizu, K. 1982: Variational Methods in Elasticity & Plasticity, Pergamon Press, Oxford

    Google Scholar 

  • Zienkiewicz, O. C.; Jain, P. C.; Oñate, E. 1977: Flow of solids during forming and extrusion: some aspects of numerical solutions. Int. J. Solid Struct. 14: 15–28

    Google Scholar 

  • Zienkiewicz, O. C.; Taylor, R. L. 1989: The Finite Element Method, 4th Edn., McGraw-Hill, New York

    Google Scholar 

  • Zienkiewicz, O. C., Vilotte, J. P.; Toyoshima, S.; Nakazawa, S. 1985: Iterative method for constrained and mixed approximation. An inexpensive improvement of FEM performance. Comp. Meth. Appl. Mech. Engrg. 51: 3–29

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by S. N. Atluri, 18 August 1995

Dedicated to J. C. Simo

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dvorkin, E.N., Cavaliere, M.A. & Goldschmit, M.B. A three field element via Augmented Lagrangian for modelling bulk metal forming processes. Computational Mechanics 17, 1–9 (1995). https://doi.org/10.1007/BF00356474

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00356474

Keywords

Navigation