Publicou 6 edições por ano
ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352
Indexed in
NONLOCAL/COARSE-GRAINING HOMOGENIZATION OF LINEAR ELASTIC MEDIA WITH NON-SEPARATED SCALES USING LEAST-SQUARE POLYNOMIAL FILTERS
RESUMO
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.
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Tognevi A., Guerich M., Yvonnet J., A multi-scale modeling method for heterogeneous structures without scale separation using a filter-based homogenization scheme, International Journal for Numerical Methods in Engineering, 108, 1, 2016. Crossref
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Misra Anil, Placidi Luca, Scerrato Daria, A review of presentations and discussions of the workshop Computational mechanics of generalized continua and applications to materials with microstructure that was held in Catania 29–31 October 2015, Mathematics and Mechanics of Solids, 22, 9, 2017. Crossref
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References, in Topology Optimization Design of Heterogeneous Materials and Structures, 2019. Crossref
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Yvonnet Julien, When Scales Cannot Be Separated: Direct Solving of Heterogeneous Structures with an Advanced Multiscale Method, in Computational Homogenization of Heterogeneous Materials with Finite Elements, 258, 2019. Crossref
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Wangermez Maxence, Allix Olivier, Guidault Pierre-Alain, Ciobanu Oana, Rey Christian, Interface coupling method for the global–local analysis of heterogeneous models: A second-order homogenization-based strategy, Computer Methods in Applied Mechanics and Engineering, 365, 2020. Crossref
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Wangermez Maxence, Allix Olivier, Guidault Pierre-Alain, Ciobanu Oana, Rey Christian, Non-intrusive global-local analysis of heterogeneous structures based on a second-order interface coupling, Computational Mechanics, 69, 5, 2022. Crossref