Kriging-based approximate stochastic homogenization analysis for composite materials

This paper describes a novel method for a stochastic analysis of a multiscale homogenization problem. An inhomogeneous material such as a composite material has a complex microstructure, and sometimes it has an uncertainty in geometry or a material property of a microstructure. This microscopic uncertainty will cause dispersion of a macroscopic homogenized material property of a composite material. In order to analyze this problem, an approximation-based stochastic analysis approach is developed. The proposed method uses a flexible approximation technique and variable transformation of a probabilistic density function. In this paper, the Kriging method is used for approximation and integral estimation of a probabilistic density function. As a numerical example, a stochastic response analysis for a homogenized elastic tensor and homogenized elastic constants of a unidirectional fiber reinforced composite material is performed using the Monte-Carlo simulation, the perturbation-based homogenization method and the proposed method. Uncertainties in material properties and geometry of a microstructure of a unidirectional fiber reinforced composite plate are taken into account. From the numerical results, validity and effectiveness of the proposed method are shown. (C) 2007 Elsevier B.V. All rights reserved.