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
JournalInternational Journal for Numerical Methods in Engineering
DOIs
Publication statusAccepted/In press - 2016

Fingerprint

Fictitious Domain Method
High-order Methods
Model Reduction
Stochastic models
Stochastic Model
Effective Properties
Prediction
Microstructure
Numerical Verification
Deterministic Model
Reduction Method
Bone
Convergence Properties
Material Properties
Probability density function
Confidence
Computational Cost
Materials properties
Decomposition
Feedback

Keywords

  • Fictitious domain method
  • High-order
  • Homogenization
  • Proper generalized decomposition
  • Stochastic

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

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N2 - 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.

AB - 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.

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