NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 51 (11-12), 2014 DOI: 10.1016/j.ijsolstr.2014.02.029
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[en] In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin components, such as cell walls or cell struts, can occur. Even if the behavior of the materials of which the micro–structure is made remains elliptic, the homogenized behavior can lose its ellipticity. In that case, a localization band is formed and propagates at the macro–scale. When the localization occurs, the assumption of local action in the standard approach, for which the stress state on a material point depends only on the strain state at that point, is no–longer suitable, which motivates the use of the second-order multi–scale computational homogenization scheme. At the macro–scale of this scheme, the discontinuous Galerkin method is chosen to solve the Mindlin strain gradient continuum.
At the microscopic scale, the classical finite element resolutions of representative volume elements are considered. Since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general, the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method. With the presence of instability phenomena at both scales, the arc–length path following technique is adopted to solve both macroscopic and microscopic problems.
ARC 09/14-02 BRIDGING - From imaging to geometrical modelling of complex micro structured materials: Bridging computational engineering and material science
Funders :
DGENORS - Communauté française de Belgique. Direction générale de l’Enseignement non obligatoire et de la Recherche scientifique
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