An adaptive multiscale method for quasi-static crack growth
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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.
KeywordsMultiscale 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.
- 1.Van Swygenhoven H, Derlet PM, Hasnaoui A (2005) Atomistic modeling of strength of nanocrystalline metals. Nanomaterials by severe plastic deformation, pp. 597–608Google Scholar
- 2.Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Proc Natl Acad Sci 73(6):1529–1563Google Scholar
- 4.Sun Y, Peng Q, Lu G (2012) Hydrogen assisted cracking: a QCDFT study of Aluminum crack-tip. submitted to PRL, December 10Google Scholar
- 7.Guidault P-A, Belytschko T (2007) On the \(L^2\) and the \(H^1\) couplings for an overlapping domain decomposition method using Lagrange multipliers. Int J Numer Methods Eng 70:322–350Google Scholar
- 8.Guidault P-A, Belytschko T (2009) Bridging domain methods for coupled atomisticcontinuum models with \(L^2\) or \(H^1\) couplings. Int J Numer Methods Eng 77(4–5):1566–1592 Google Scholar
- 9.Gracie Robert, Belytschko Ted (2008) Concurrently coupled atomistic and XFEM models for dislocations and cracks. Intl J Numer Methods Eng 78(3):354–378Google Scholar
- 16.Qian D, Wagner GJ, Liu WK (2003) A multiscale projection method for the analysis of carbon nanotubes. Comput Methods Appl Mech Eng 193(17–20):1603–1632Google Scholar
- 17.Song JH, Areias PMA, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67:868–893 Google Scholar
- 18.Ye Y, Shardool C, David NA, Thomas E, Stephen S, Dong Q (2011) Enriched spacetime finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics. Int J Numer Methods Eng 92(2), 115–140Google Scholar