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Concurrently coupled atomistic and XFEM models for dislocations and cracks. (English) Zbl 1183.74278
Summary: 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.
MSC:
74S05Finite element methods in solid mechanics
74R10Brittle fracture
74A25Molecular, statistical, and kinetic theories (mechanics of deformable solids)
Software:
L-BFGS