Simulations of micron-scale fracture using atomistic-based boundary element method

A new formulation of a boundary element method (BEM) is proposed in this paper to simulate cracks at the micron scale. The main departure from the traditional BEMs is that the current model is derived from the underlying atomistic model, which involves the interactions of atoms at the scale of Angstroms. By using the lattice Green's function, the new BEM formulation eliminates the excessive atomic degrees of freedom away from crack tips, and directly couples the process zones with the physical boundary conditions. We show that with such a drastic reduction, one can simulate brittle fracture process on the scale of microns, for which the entire system consists of a few billion atoms. We discuss several numerical issues to make the implementation more efficient. Examples will be presented for cracks in the bcc iron system.