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Abstract: Functionally graded materials FGMs are two-phase composites withcontinuously changing microstructure adapted to performance requirements.Traditionally, the overall behavior of FGMs has been determined using localaveraging techniques or a given smooth variation of material properties.Although these models are computationally efficient, their validity andaccuracy remain questionable, since a link with the underlying microstructureincluding its randomness is not clear. In this paper, we propose a modelingstrategy for the linear elastic analysis of FGMs systematically based on arealistic microstructural model. The overall response of FGMs is addressed inthe framework of stochastic Hashin-Shtrikman variational principles. To allowfor the analysis of finite bodies, recently introduced discretization schemesbased on the Finite Element Method and the Boundary Element Method are employedto obtain statistics of local fields. Representative numerical examples arepresented to compare the performance and accuracy of both schemes. To gaininsight into similarities and differences between these methods and to minimizetechnicalities, the analysis is performed in the one-dimensional setting.



Author: Zahra Sharif-Khodaei, Jan Zeman

Source: https://arxiv.org/







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