International Journal of Material Forming

, Volume 7, Issue 3, pp 337–358 | Cite as

POD surrogates for real-time multi-parametric sheet metal forming problems

  • M. Hamdaoui
  • G. Le Quilliec
  • P. Breitkopf
  • P. Villon
Original Research


Our approach aims at coupling the ever increasing off-line computing power of mainframe computers with the interactive on-line possibilities of ubiquitous low computing power devices at the early design stages in order to provide insight into the design problems and to search for candidate optimal design points. In the off-line phase, the method under investigation relies on combining an optimized space-filling sampling plan on the design parameter space with extensive finite elements (FE) simulations yielding a learning set of displacement fields. The objective of this paper is the on-line phase. We provide a rigorous mathematical presentation of a family of non-intrusive, bi-level surrogates. We focus on displacement field approximation by Proper Orthogonal Decomposition (POD) combined with kriging interpolation of coefficients. The method is illustrated with two simple, easily reproduced numerical examples of quality assessment of deep-drawing process of a cylindrical cup by on-the-fly plotting forming limit diagrams (FLDs) and related quantities enabling thus to spot improved design points.


POD Interpolation Kriging Sheet metal forming Real-time Non-intrusive 



Emmanuel Le Franois, lecturer at Roberval Laboratory is acknowledged for his advices about the finite elements method. This research was conducted as part of the OASIS project, supported by OSEO within the contract FUI no. F1012003Z. This work was carried out in the framework of the Labex MS2T, which is funded by the French Government, through the program ”Investments for the future” managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02).


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Copyright information

© Springer-Verlag France 2013

Authors and Affiliations

  • M. Hamdaoui
    • 1
  • G. Le Quilliec
    • 1
  • P. Breitkopf
    • 1
  • P. Villon
    • 1
  1. 1.Laboratoire Roberval UMR 7337 UTC-CNRSCompiegne cedexFrance

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