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Stochastic Upscaling via Linear Bayesian Updating

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Multiscale Modeling of Heterogeneous Structures

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 86))

Abstract

In this work we present an upscaling technique for multi-scale computations based on a stochastic model calibration technique. We consider a coarse scale continuum material model described in the framework of generalised standard materials. The model parameters are considered uncertain in this approach, and are approximated using random variables. The update or calibration of these random variables is performed in a Bayesian framework where the information from a deterministic fine scale model computation is used as observation. The proposed approach is independent w.r.t. the choice of models on coarse and fine scales. Simple numerical examples are shown to demonstrate the ability of the proposed approach to calibrate coarse-scale elastic and inelastic material parameters.

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Acknowledgements

This paper is based upon work supported by DFG (Deutsche Forschungsgemeinschaft), Germany, and ANR (Agence Nationale de la Recherche), France, under the grant of the SELF-TUM project.

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Authors and Affiliations

  1. Institute of Scientic Computing, TU Braunschweig, Braunschweig, Germany

    Sadiq M. Sarfaraz, Bojana V. Rosić & Hermann G. Matthies

  2. Laboratoire Roberval, UTC Compiègne, Compiègne, France

    Adnan Ibrahimbegović

Authors
  1. Sadiq M. Sarfaraz
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  2. Bojana V. Rosić
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  3. Hermann G. Matthies
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  4. Adnan Ibrahimbegović
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Correspondence to Sadiq M. Sarfaraz .

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Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Jurica Sorić

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

  3. LMT Cachan, Cachan, France

    Olivier Allix

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Sarfaraz, S.M., Rosić, B.V., Matthies, H.G., Ibrahimbegović, A. (2018). Stochastic Upscaling via Linear Bayesian Updating. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-65463-8_9

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