Vol. 3, No. 9, 2008

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Microstructure-based modeling of elastic functionally graded materials: One-dimensional case

Zahra Sharif-Khodaei and Jan Zeman

Vol. 3 (2008), No. 9, 1773–1796

Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or a given smooth variation of material properties. Although these models are computationally efficient, their validity and accuracy remain questionable, since a link with the underlying microstructure (including its randomness) is not clear. In this paper, we propose a numerical modeling strategy for the linear elastic analysis of FGMs systematically based on a realistic microstructural model. The overall response of FGMs is addressed in the framework of stochastic Hashin–Shtrikman variational principles. To allow for the analysis of finite bodies, recently introduced discretization schemes based on the finite element method and the boundary element method are employed to obtain statistics of local fields. Representative numerical examples are presented to compare the performance and limitations of both schemes. To gain insight into similarities and differences between these methods and to minimize technicalities, the analysis is performed in the one-dimensional setting.

functionally graded materials, statistically nonuniform composites, microstructural model of fully penetrable spheres, Hashin–Shtrikman variational principles, finite element method, boundary element method
Received: 26 August 2008
Revised: 27 October 2008
Accepted: 1 November 2008
Published: 1 November 2008
Zahra Sharif-Khodaei
Faculty of Civil Engineering
Department of Mechanics
Czech Technical University in Prague
Thakurova 7
Prague 6, 166 29
Czech Republic
Department of Aeronautics
Imperial College London
Prince Consort Road
London SW7 2AZ
Great Britain
Jan Zeman
Faculty of Civil Engineering
Department of Mechanics
Czech Technical University in Prague
Thakurova 7
Prague 6, 166 29
Czech Republic