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

Grégory Legrain (1) , Mathilde Chevreuil (1) , Naoki Takano (2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 Faculty of Science and Technology, Keio University

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: (i) a high-order fictitious domain method; (ii) an accurate spectral stochastic model and (iii) 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.

Mots clés: proper generalized decomposition; stochastic; fictitious domain method; homogenization; high-order

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Grégory Legrain, Mathilde Chevreuil, Naoki Takano. Prediction of apparent properties with uncertain material parameters using high-order fictitious domain methods and PGD model reduction. International Journal for Numerical Methods in Engineering, 2016, ⟨10.1002/nme.5289⟩. ⟨hal-01303388⟩