Computational Mechanics

, Volume 53, Issue 6, pp 1129–1148 | Cite as

An adaptive multiscale method for quasi-static crack growth

  • Pattabhi R. Budarapu
  • Robert Gracie
  • Stéphane P.A. Bordas
  • Timon RabczukEmail author
Review Paper


This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.


Multiscale Adaptivity Refinement Coarsening Phantom node method Molecular statics Virtual atom cluster. 



The support provided by the DeutscheForschungsgemeinschaft (DFG) is gratefully acknowledged. The financial support from the IRSES is thankfully acknowledged. Dr. Gracie’s research was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. Technical inputs from Prof. Stéphane Bordas of Cardiff University are gladly acknowledged. Technical interactions with Professor Qian Dong of University of Texas at Dallas and Dr. Cosmin Anitescu of Bauhaus University of Weimar are gratefully acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pattabhi R. Budarapu
    • 1
  • Robert Gracie
    • 2
  • Stéphane P.A. Bordas
    • 3
  • Timon Rabczuk
    • 1
    • 4
    Email author
  1. 1.Institute of Structural MechanicsBauhaus Univesity of WeimarWeimarGermany
  2. 2.Department of Civil and Environmental EngineeringUniversity of WaterlooWaterlooCanada
  3. 3.Institute of Mechanics and Advanced MaterialsCardiff UniversityCardiffWales, UK
  4. 4.School of Civil, Environmental and Architectural EngineeringKorea UniversitySeoulKorea

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