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Prediction of apparent properties with uncertain material parameters using high‐order fictitious domain methods and PGD model reduction
Author(s) -
Legrain Gregory,
Chevreuil Mathilde,
Takano Naoki
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5289
Subject(s) - model order reduction , reduction (mathematics) , convergence (economics) , mathematical optimization , mathematics , computer science , domain (mathematical analysis) , function (biology) , stochastic modelling , algorithm , mathematical analysis , statistics , projection (relational algebra) , geometry , economics , economic growth , evolutionary biology , biology
Summary 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. Copyright © 2016 John Wiley & Sons, Ltd.