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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2014010414
pages 375-395

NONLOCAL/COARSE-GRAINING HOMOGENIZATION OF LINEAR ELASTIC MEDIA WITH NON-SEPARATED SCALES USING LEAST-SQUARE POLYNOMIAL FILTERS

Julien Yvonnet
Universite Paris-Est, Laboratoire Modelisation et simulation Multi Echelle, 5 Bd Descartes, F-77454 Marne-la-Vallee Cedex 2, France
Guy Bonnet
Universite Paris-Est, Laboratoire Modelisation et simulation Multi Echelle, 5 Bd Descartes, F-77454 Marne-la-Vallee Cedex 2, France

ABSTRACT

In this paper, a nonlocal computational method is proposed to construct a mesoscopic (coarse-grained) model of linear elastic heterogeneous materials in the case of nonseparated scales. The framework, introduced in our previous paper (Yvonnet and Bonnet, 2014), extends the classical homogenization framework by using low-pass filters operators instead of averaging operators, and Green's nonlocal functions instead of localization operators. In the present work, we introduce a filtering procedure based on least-square polynomial approximation to avoid the numerical drawbacks of Gaussian filters infinite domains. The complete associated homogenization scheme is described, as well as a numerical procedure based on finite elements to compute the different homogenized operators from a unit cell. The methodology is validated by analyzing both local and mesoscopic mechanical fields in structures where heterogeneities are of comparable size with respect to the loading characteristic fluctuation wavelength.