Multi-scale computational homogenization: Trends and challenges

Authors:
M. G. D. Geers;V. G. Kouznetsova;W. A. M. Brekelmans
Affiliations:
Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands;Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands and Materials Innovation Institute, Mekelweg 2, 2628 CD Delft, The Nether ...;Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In the past decades, considerable progress had been made in bridging the mechanics of materials to other disciplines, e.g. downscaling to the field of materials science or upscaling to the field of structural engineering. Within this wide context, this paper reviews the state-of-the-art of a particular, yet powerful, method, i.e. computational homogenization. The paper discusses the main trends since the early developments of this approach up to the ongoing contributions and upcoming challenges in the field.