A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials

Authors:
X. Frank Xu;Xi Chen;Lihua Shen
Affiliations:
Department of Civil, Environmental, and Ocen Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA;Department of Civil, Environmental, and Ocen Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA;Department of Civil, Environmental, and Ocen Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA and Institute of Mathematics and Interdisciplinary Science, College of Mathematica ...
Venue:
Computers and Structures
Year:
2009

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Abstract

Classical continuum theories are formulated based on the assumption of large scale separation. For scale-coupling problems involving uncertainties, novel multiscale methods are desired. In this study, by employing the generalized variational principles, a Green-function-based multiscale method is formulated to decompose a boundary value problem with random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering practices by smearing out fine-scale microstructures. The fast scale problem evaluates fluctuations due to random microstructures, which is important for scale-coupling systems and particularly failure problems. Two numerical examples are provided at the end.