Prediction of apparent properties with uncertain material parameters using high-order fictitious domain methods and PGD model reduction

Gregory Legrain, Mathilde Chevreuil, Naoki Takano

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This contribution presents a numerical strategy to evaluate the effective properties of image-based microstructures in the case of random material properties. The method relies on three points: (1) a high-order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model-reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained.

Original languageEnglish
Pages (from-to)345-367
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Volume109
Issue number3
DOIs
Publication statusPublished - 2017 Jan 20

Keywords

  • fictitious domain method
  • high-order
  • homogenization
  • proper generalized decomposition
  • stochastic

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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