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Novel boundary conditions for strain localization analyses in microstructural volume elements
Author(s) -
Coenen E.W.C.,
Kouznetsova V.G.,
Geers M.G.D.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3298
Subject(s) - representative elementary volume , boundary (topology) , materials science , boundary value problem , deformation (meteorology) , spurious relationship , mechanics , stiffness , percolation (cognitive psychology) , mathematical analysis , physics , composite material , computer science , mathematics , microstructure , biology , machine learning , neuroscience
SUMMARY Multi‐scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted. In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation‐path‐aligned boundary conditions . Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto‐plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure. Copyright © 2011 John Wiley & Sons, Ltd.