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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013005569
pages 565-580


Mirmohammadreza Kabiri
Department of Civil, Environmental and Architectural Engineering, Program of Material Science and Engineering, University of Colorado, Boulder, Colorado, USA
Franck J. Vernerey
Department of Civil, Environmental and Architectural Engineering, Program of Material Science and Engineering, University of Colorado, Boulder, Colorado, USA


This paper introduces a concurrent adaptive multiscale methodology in which both macroscopic and microscopic deformation fields strongly interact. The method is based on the balance between numerical and homogenization error; while the first type of error states that the element's should be refined in regions of high deformation gradients, the second implies that elements size may not be smaller than a threshold determined by the size of the representative volume element (RVE). In this context, we introduce a multiscale method in which RVEs can be embedded in the continuum region through appropriate macro-micro boundary coupling conditions. By combining the idea of adaptive refinement with the embedded RVE method, the methodology ensures that appropriate descriptions of the material are used adequately, regardless of the severity of deformations. We show that this method, in conjunction with the extended finite element method, is ideal to study the strong interactions between a crack and the microstructure of heterogeneous media. In particular, the method enables an explicit description of microstructural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. We illustrate the method with several examples showing its accuracy and relatively low computational cost and discuss its potential in relating microstructure to the fracture toughness of a diversity of heterogeneous media.


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