Unpublished conference/Abstract (Scientific congresses and symposiums)
Computational homogenization of cellular materials with propagation of instabilities through the scales
Nguyen, Van Dung; Noels, Ludovic
2014EMMC14 - European Mechanics of Materials Conference 2014
Peer reviewed
 

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Keywords :
cellular; multiscale; computational homogenization
Abstract :
[en] The aim of this work is to develop an efficient multi–scale finite element framework to capture the buckling instabilities in cellular materials. As a classical multi–scale computational homogenization scheme looses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second–order multi–scale computational homogenization scheme1 is considered. This second–order computational framework is herein enhanced with the following novelties so that it can be used for cellular materials. First, at the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity3. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems4. The micro–buckling leading to the macroscopic localization and the size effect phenomena can be captured within the proposed framework. In particular it is shown that results are not dependent on the mesh size at the macroscopic scale during the softening response, and that they agree well with the direct numerical simulations.
Disciplines :
Mechanical engineering
Materials science & engineering
Author, co-author :
Nguyen, Van Dung  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
Computational homogenization of cellular materials with propagation of instabilities through the scales
Publication date :
29 August 2014
Event name :
EMMC14 - European Mechanics of Materials Conference 2014
Event organizer :
EuroMech
Event place :
Gothenburg, Sweden
Event date :
27 - 29 August, 2014
Audience :
International
Peer reviewed :
Peer reviewed
Name of the research project :
ARC 09/14-02 BRIDGING
Funders :
FWB - Fédération Wallonie-Bruxelles [BE]
Available on ORBi :
since 10 September 2014

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