A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework

This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE 2 ) towards a discontinuity enriched framework. The classical homogenization approaches typically rely...

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Bibliographic Details
Published in:International journal of fracture 2012-11, Vol.178 (1-2), p.157-178
Main Authors: Coenen, E. W. C., Kouznetsova, V. G., Bosco, E., Geers, M. G. D.
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Boundary value problems
Bridge failure
Characterization and Evaluation of Materials
Chemistry and Materials Science
Civil Engineering
Classical Mechanics
Computation
Crack propagation
Damage localization
Deformation
Discontinuity
Homogenization
Localization
Materials Science
Mechanical Engineering
Microstructure
Multiscale analysis
Original Paper
Strain localization
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Summary:This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE 2 ) towards a discontinuity enriched framework. The classical homogenization approaches typically rely on the separation of scales principle, which is violated as soon as a strain localization band develops within a microstructural volume element (MVE). The newly developed scheme resolves this limitation by considering the bifurcation of the microscale deformation into a continuum ‘bulk’ part and a localization related part. The most distinct feature of the proposed framework is that both, the local macroscale traction-opening response of the cohesive crack and the stress-strain response of the surrounding ‘bulk’, are obtained from a single MVE analysis. The discontinuity enriched macroscale description is formulated to accommodate for the micro-macro coupling. The macroscale boundary value problem and the corresponding implementation are detailed for the use within the embedded discontinuities approach. The presented multi-scale method is demonstrated on a numerical example of a cohesive crack propagation in a macroscopic double notch specimen, with underlying voided microstructure.
ISSN:0376-9429
1573-2673
DOI:10.1007/s10704-012-9765-4