Open Access

ARTICLE

A Discrete Fourier Transform Framework for Localization Relations

D.T. Fullwood¹, S.R. Kalidindi², B.L. Adams¹, S. Ahmadi¹

1 BYU, Provo, UT, U.S.A.
2 Drexel, Philadelphia, PA, U.S.A

Computers, Materials & Continua 2009, 9(1), 25-40. https://doi.org/10.3970/cmc.2009.009.025

Abstract

Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green's function integrals are resolved, and the method is validated against finite element analysis.

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Keywords

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