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

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.