Computational homogenization

M.G.D. Geers, V. Kouznetsova, W.A.M. Brekelmans

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

29 Citations (Scopus)
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This part of the CISM course addresses basics and advanced topics onthe computational homogenization of the mechanics of highly non-linear solids with(possibly evolving) microstructure under complex non-linear loading conditions.The key components of the computational homogenization scheme, i.e. the formulationof the microstructural boundary value problem and the coupling betweenthe micro and macrolevel based on the averaging theorems, are addressed. Thenumerical implementation of the framework, particularly the computation of themacroscopic stress tensor and extraction of the macroscopic consistent tangent operatorbased on the total microstructural stiffness, are treated in detail. The applicationof the method is illustrated by the simulation of pure bending of porousaluminum. The classical notion of a representative volume element is introducedand the influence of the spatial distribution of heterogeneities on the overall macroscopicbehaviour is investigated by comparing the results of multi-scale modellingfor regular and random structures. Finally, an extension of the classical computationalhomogenization scheme to a framework suitable for multi-scale modelling ofmacroscopic localization and size effects is briefly discussed.
Original languageEnglish
Title of host publicationMultiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics, CISM Courses and Lectures, vol. 522
EditorsR. Pippan, P. Gumbsch
Place of PublicationWien New York
ISBN (Print)978-3-7091-0282-4
Publication statusPublished - 2010

Publication series

NameCISM International Centre for Mechanical Sciences
ISSN (Print)0254-1971


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