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Concurrently coupled atomistic and XFEM models for dislocations and cracks
Author(s) -
Gracie Robert,
Belytschko Ted
Publication year - 2008
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.2488
Subject(s) - lagrange multiplier , materials science , domain decomposition methods , finite element method , statistical physics , dislocation , slip (aerodynamics) , physics , condensed matter physics , thermodynamics , quantum mechanics
A method for the modeling of dislocations and cracks by atomistic/continuum models is described. The methodology combines the extended finite element method with the bridging domain method (BDM). The former is used to model crack surfaces and slip planes in the continuum, whereas the BDM is used to link the atomistic models with the continuum. The BDM is an overlapping domain decomposition method in which the atomistic and continuum energies are blended so that their contributions decay to their boundaries on the overlapping subdomain. Compatibility between the continua and atomistic domains is enforced by a continuous Lagrange multiplier field. The methodology allows for simulations with atomistic resolution near crack fronts and dislocation cores while retaining a continuum model in the remaining part of the domain and so a large reduction in the number of atoms is possible. It is applied to the modeling of cracks and dislocations in graphene sheets. Energies and energy distributions compare very well with direct numerical simulations by strictly atomistic models. Copyright © 2008 John Wiley & Sons, Ltd.