International Journal of Material Forming

, Volume 7, Issue 3, pp 275–287

A two-pronged approach for springback variability assessment using sparse polynomial chaos expansion and multi-level simulations

  • Jérémy Lebon
  • Guénhaël Le Quilliec
  • Piotr Breitkopf
  • Rajan Filomeno Coelho
  • Pierre Villon
Original Research

DOI: 10.1007/s12289-013-1126-y

Cite this article as:
Lebon, J., Le Quilliec, G., Breitkopf, P. et al. Int J Mater Form (2014) 7: 275. doi:10.1007/s12289-013-1126-y
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Abstract

In this study, we show that stochastic analysis of metal forming process requires both a high precision and low cost numerical models in order to take into account very small perturbations on inputs (physical as well as process parameters) and to allow for numerous repeated analysis in a reasonable time. To this end, an original semi-analytical model dedicated to plain strain deep drawing based on a Bending-Under-Tension numerical model (B-U-T model) is used to accurately predict the influence of small random perturbations around a nominal solution estimated with a full scale Finite Element Model (FEM). We introduce a custom sparse variant of the Polynomial Chaos Expansion (PCE) to model the propagation of uncertainties through this model at low computational cost. Next, we apply this methodology to the deep drawing process of U-shaped metal sheet considering up to 8 random variables.

Keywords

Springback variability assessment Sparse polynomial chaos expansion Semi-analytical bending-under-tension model 

Copyright information

© Springer-Verlag France 2013

Authors and Affiliations

  • Jérémy Lebon
    • 1
    • 2
  • Guénhaël Le Quilliec
    • 1
  • Piotr Breitkopf
    • 1
  • Rajan Filomeno Coelho
    • 2
  • Pierre Villon
    • 1
  1. 1.Laboratoire Roberval, UMR 7337Université de Technologie de CompiègneCompiègne cedexFrance
  2. 2.BATir Department CP 194/2Université Libre de Bruxelles (ULB)BrusselsBelgium

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