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

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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.

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Acknowledgments

This research was conducted as part of the OASIS project, supported by OSEO within the contract FUI no. F1012003Z. The first author is grateful to Innoviris for its support to BB2B project entitled multicriteria optimization with uncertainty quantification applied to the building industry. The authors also acknowledge the support of Labex MS2T.

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Authors and Affiliations

  1. Laboratoire Roberval, UMR 7337, Université de Technologie de Compiègne, BP 20529, 60205, Compiègne cedex, France

    Jérémy Lebon, Guénhaël Le Quilliec, Piotr Breitkopf & Pierre Villon

  2. BATir Department CP 194/2, Université Libre de Bruxelles (ULB), 50, avenue Franklin Roosevelt, 1050, Brussels, Belgium

    Jérémy Lebon & Rajan Filomeno Coelho

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  1. Jérémy Lebon
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  2. Guénhaël Le Quilliec
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  3. Piotr Breitkopf
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  4. Rajan Filomeno Coelho
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  5. Pierre Villon
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Correspondence to Jérémy Lebon.

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Lebon, J., Le Quilliec, G., Breitkopf, P. et al. A two-pronged approach for springback variability assessment using sparse polynomial chaos expansion and multi-level simulations. Int J Mater Form 7, 275–287 (2014). https://doi.org/10.1007/s12289-013-1126-y

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  • DOI: https://doi.org/10.1007/s12289-013-1126-y

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