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

作者：Coenen E W C; Kouznetsova V G^*; Bosco E; Geers M G D

来源：International Journal of Fracture, 2012, 178(1-2): 157-178.

DOI：10.1007/s10704-012-9765-4

• Multi-scale modelling
• Computational homogenization
• Strain localization
• Damage and failure
• Cohesive crack
• Microstructural volume element

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 %26apos;bulk%26apos; 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 %26apos;bulk%26apos;, 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.

• 出版日期2012-11