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

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Abstract

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 (FE2) 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.

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Authors and Affiliations

  1. Materials innovation institute (M2i), P.O. Box 5008, 2600 GA, Delft, The Netherlands

    E. W. C. Coenen

  2. Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands

    E. W. C. Coenen, V. G. Kouznetsova & M. G. D. Geers

  3. Department of Mathematics, Faculty of Engineering, University of Brescia, via D Valotti 9, 25133, Brescia, Italy

    E. Bosco

Authors
  1. E. W. C. Coenen
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  2. V. G. Kouznetsova
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  3. E. Bosco
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  4. M. G. D. Geers
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Correspondence to V. G. Kouznetsova.

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Coenen, E.W.C., Kouznetsova, V.G., Bosco, E. et al. A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework. Int J Fract 178, 157–178 (2012). https://doi.org/10.1007/s10704-012-9765-4

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  • DOI: https://doi.org/10.1007/s10704-012-9765-4

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