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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v2.i4.50
24 pages

Size of a Representative Volume Element in a Second-Order Computational Homogenization Framework

Varvara G. Kouznetsova
Department of Mechanical Engineering, Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven; and Netherlands Institute for Metals Research, Rotterdamseweg 137 2628 AL Delft, The Netherlands
Marc Geers
Dept. of Mechanical Engineering Eindhoven University of Technology PO Box 513, 5600 MB Eindhoven The Netherlands
W. A. M. Brekelmans
Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Краткое описание

In this paper the intrinsic role of the size of the microstructural representative volume element (RVE) in a second-order computational homogenization is investigated. The presented second-order computational homogenization is an extension of the classical first-order computational homogenization scheme and is based on a proper incorporation of the macroscopic gradient of the deformation tensor and the associated higher-order stress measure into the multiscale framework. The macroscopic homogenized continuum obtained through this scheme is the full second gradient continuum. It is demonstrated with several examples that the size of the microstructural RVE used in a second-order computational homogenization scheme may be related to the length scale of the associated macroscopic homogenized higher-order continuum. It is shown that the analytical second-order homogenization of a microstructurally homogeneous linearly elastic material leads to the second gradient elastic Mindlin's continuum on the macroscale, where the resulting macroscopic length scale parameter is proportional to the RVE size. Several numerical microstructural and multiscale analyses reveal the significance of the contribution of the physical and geometrical nonlinearities in the relation between the RVE size and the calculated macroscopic response. Based on the obtained results, some conclusions are drawn with respect to the choice of the microstructural RVE in the second-order computational homogenization analysis.