Skip to main content
Log in

Detection of strain localization in numerical simulation of sheet metal forming

  • Original Research Article
  • Published:
Archives of Civil and Mechanical Engineering Aims and scope Submit manuscript


This paper presents an investigation on the detection of strain localization in numerical simulation of sheet metal forming. Two methods to determine the onset of localized necking have been compared. The first criterion, newly implemented in this work, is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method, studied in the authors’ earlier works, is determined by the maximum of the strain acceleration. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has allowed to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one. Mesh sensitivity analysis for these criteria has been performed for the selected specimens. It has been shown that the numerical FLC obtained with the new criterion predicts formability limits close to the experimental results so this method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others


  1. R.E. Dick, J.W. Yoon, T.B. Stoughton, Path-independent forming limit models for multi-stage forming processes, Int. J. Mater. Form. (2015) 1–11.

  2. J. Zhang, Y. Xu, P. Hu, K. Zhao, Development and applications of forming-condition-based formability diagram for split concerns in stamping, J. Manuf. Processes 17 (2015) 151–161.

    Article  Google Scholar 

  3. M. Abspoel, M.E. Scholting, J.M. Droog, A new method for predicting forming limit curves from mechanical properties, J. Mater. Process. Technol. 213 (5) (2013) 759–769.

    Article  Google Scholar 

  4. ISO 20482, Metallic Materials — Sheet and Strip — Erichsen Cupping Test, 2003.

  5. ISO 12004-2, Metallic Materials — Sheet and Strip — Determination of Forming-Limit Curves. Part 2: Determination of Forming-Limit Curves in the Laboratory, 2008.

  6. D. Banabic, L. Lazarescu, L. Paraianu, I. Ciobanu, I. Nicodim, D. Comsa, Development of a new procedure for the experimental determination of the forming limit curves, CIRP Ann. Manuf. Technol. 62 (1) (2013) 255–258.

    Article  Google Scholar 

  7. H.W. Swift, Plastic instability under plane stress, J. Mech. Phys. Solids 1 (1) (1952) 1–18.

    Article  MathSciNet  Google Scholar 

  8. R. Hill, On discontinuous plastic states with special reference to localized necking in thin sheets, J. Mech. Phys. Solids 1 (1952) 19–30.

    Article  MathSciNet  Google Scholar 

  9. Z. Marciniak, Stability of plastic shells under tension with kinematic boundary condition, Arch. Mech. Stosorwanej 17 (1994) 577–592.

    Google Scholar 

  10. Q. Situ, M. Jain, D. Metzger, Determination of forming limit diagrams of sheet materials with a hybrid experimental- numerical approach, Int. J. Mech. Sci. 53 (4) (2011) 707–719.

    Article  Google Scholar 

  11. D. Banabic, Sheet Metal Forming Processes Constitutive Modelling and Numerical Simulation, Springer, 2010.

  12. D. Banabic, A review on recent developments of Marciniak—Kuczynski model, Comput. Methods Mater. Sci. 10 (4) (2010) 225–237.

    Google Scholar 

  13. C. Veerman, P.F. Neve, Some aspects of the determination of the FLD-onset of localized necking, Sheet Metal Ind. 49 (1972) 421–423.

    Google Scholar 

  14. R. d’Hayer, A. Bragard, Determination of the limiting strains at the onset of necking, Centre Res. Metall. 42 (1975) 33–35.

    Google Scholar 

  15. T. Kobayashi, H. Ishigaki, A. Tadayuki, Effect of strain ratios on the deforming limit of steel sheet and its application to the actual press forming, in: Proceedings of the IDDRG Congress, 1972, pp. 8.1–8.4.

  16. S.S. Hecker, Simple technique for determining forming limit curves, Sheet Metal Ind. 5 (1975) 671–676.

    Google Scholar 

  17. W. Volk, P. Hora, New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination, Int. J. Mater. Form. 4 (3) (2011) 339–346.

    Article  Google Scholar 

  18. Q. Situ, M. Jain, M. Bruhis, A suitable criterion for precise determination of incipient necking in sheet materials, Mater. Sci. Forum 519–521 (2006) 111–116.

    Article  Google Scholar 

  19. Z. Zimniak, Nowa metoda wyznaczania utraty stateczności blachy oraz napręŜeń szczątkowych, in: Proceedings of FORMING’2002, 2002, 333–338.

  20. H. Mamusi, A. Masoumi, R. Mahdavinezhad, Numerical simulation for the formability prediction of the laser welded blanks (TWB), Int. J. Mech. Aerosp. Ind. Mechatron. Manuf. Eng. 6 (7) (2012) 111–116.

    Google Scholar 

  21. D. Lumelskyy, J. Rojek, P.R.F. Grosman, M. Tkocz, Numerical simulation of formability tests of pre-deformed steel blanks, Arch. Civil Mech. Eng. 12 (2) (2012) 133–141.

    Article  Google Scholar 

  22. D. Lumelskyj, J. Rojek, M. Tkocz, Numerical simulations of Nakazima formability tests with prediction of failure, Roman. J. Tech. Sci. Appl. Mech. 60 (3) (2015) 184–194.

    Google Scholar 

  23. D. Lumelskyj, J. Rojek, D. Banabic, L. Lazarescu, Detection of strain localization in Nakazima formability test – experimental research and numerical simulation, in: 17th International Conference on Sheet Metal, SHEMET17, Procedia Eng. 183 (2017) 89–94.

    Article  Google Scholar 

  24. D. Lumelskyy, J. Rojek, R. Pecherski, F. Grosman, M. Tkocz, W. Chorzepa, Forming limit curves for complex strain paths, Arch. Metall. Mater. 2 (58) (2013) 587–593.

    Google Scholar 

  25. J. Rojek, O. Zienkiewicz, E. Oñate, E. Postek, Advances in FE explicit formulation for simulation of metalforming processes, J. Mater. Process. Technol. 119 (1–3) (2001) 41–47.

    Article  Google Scholar 

  26. P. Kowalczyk, J. Rojek, R. Stocki, T. Bednarek, P. Tauzowski, R. Lasota, D. Lumelskyy, K. Wawrzyk, Numpress – integrated computer system for analysis and optimization of industrial sheet metal forming processes, Hutnik – Wiadomości Hutnicze 81 (1) (2014) 56–63.

    Google Scholar 

  27. J. Rojek, E. Oñate, Sheet springback analysis using a simple shell triangle with translational degrees of freedom only, Int. J. Form. Processes 1 (3) (1998) 275–296.

    Google Scholar 

  28. H. Yu, Y. Huang, Asymptotic expansion and superconvergence for triangular linear finite element on a class of typical mesh, Int. J. Numer. Anal. Model. 9 (2012) 892–908.

    MathSciNet  MATH  Google Scholar 

  29. R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. London (1948) 281–297.

  30. D. Lumelskyy, J. Rojek, R. Pecherski, F. Grosman, M. Tkocz, Influence of friction on strain distribution in Nakazima formability test of circular specimen, in: 4th International Lower Silesia – Saxony Conference on Advanced Metal Forming Processes in Automotive Industry AutoMetForm, Freiberg, 2014, 214–217.

  31. M. Jirasek, Objective modeling of strain localization, Rev. fr. genie civil 6 (2002) 1119–1132.

    Google Scholar 

  32. A. Graf, W. Hosford, Calculations of forming limit diagram for changing strain paths, Metall. Trans. A 24 (11) (1993) 2497–2501.

    Article  Google Scholar 

  33. F. Ozturk, D. Lee, Experimental and numerical analysis of out-of-plane formability test, J. Mater. Process. Technol. 170 (1–2) (2005) 247–253.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Dmytro Lumelskyj.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lumelskyj, D., Rojek, J. & Tkocz, M. Detection of strain localization in numerical simulation of sheet metal forming. Archiv.Civ.Mech.Eng 18, 490–499 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: