Multiscale analysis with atomistic/continuum models for fracture

Some of the advances and issues in multiscale analysis will be discussed. As a topic of focus, the bridging domain method for coupling continuum models with molecular models is described. In this method, the domains with different modeling methods are overlapped in a bridging subdomain, where the Hamitonian is taken to be a linear combination of the contiguous Hamiltonians. We enforce the compatibility in the bridging domain by Lagrange multipliers or by the augmented Lagrangian method. Results show that this multiscale method can avoid spurious wave reflections at the molecular/continuum interface without any additional filtering procedures, even for problems with significant nonlinearities. The method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain. A multiple-time-step algorithm has also been developed within this framework.