An adaptive multiscale method for quasi-static crack growth

Pattabhi R. Budarapu, Robert Gracie, Stéphane P.A. Bordas, Timon Rabczuk

Research output: Contribution to journalReview articlepeer-review

189 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1129-1148
Number of pages20
JournalComputational Mechanics
Issue number6
Publication statusPublished - 2014 Jun


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

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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