Statistical reconstruction and Karhunen-Loève expansion for multiphase random media

• Published in: International journal for numerical methods in engineering 2016-01, Vol.105 (1), p.3-32
• Main Authors: Feng, J. W., Cen, S., Li, C. F., Owen, D. R. J.
• Format: Article
• Language: English
• Subjects: composite material; heterogeneous material; non-Gaussian fields; random microstructure; sample reconstruction; stochastic finite element methods
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4957

Summary Termed as random media, rocks, composites, alloys and many other heterogeneous materials consist of multiple material phases that are randomly distributed through the medium. This paper presents a robust and efficient algorithm for reconstructing random media, which can then be fed into stochastic finite element solvers for statistical response analysis. The new method is based on nonlinear transformation of Gaussian random fields, and the reconstructed media can meet the discrete‐valued marginal probability distribution function and the two‐point correlation function of the reference medium. The new method, which avoids iterative root‐finding computation, is highly efficient and particularly suitable for reconstructing large‐size random media or a large number of samples. Also, benefiting from the high efficiency of the proposed reconstruction scheme, a Karhunen–Loève (KL) representation of the target random medium can be efficiently estimated by projecting the reconstructed samples onto the KL basis. The resulting uncorrelated KL coefficients can be further expressed as functions of independent Gaussian random variables to obtain an approximate Gaussian representation, which is often required in stochastic finite element analysis. Copyright © 2015 John Wiley & Sons, Ltd.