Domain reduction method for atomistic simulations

In this paper, a quasi-static formulation of the method of multi-scale boundary conditions (MSBCs) is derived and applied to atomistic simulations of carbon nano-structures, namely single graphene sheets and multi-layered graphite. This domain reduction method allows for the simulation of deformable boundaries in periodic atomic lattice structures, reduces the effective size of the computational domain, and consequently decreases the cost of computations. The size of the reduced domain is determined by the value of the domain reduction parameter. This parameter is related to the distance between the boundary of the reduced domain, where MSBCs are applied, and the boundary of the full domain, where the standard displacement boundary conditions are prescribed. Two types of multi-scale boundary conditions are derived: one for simulating in-layer multi-scale boundaries in a single graphene sheet and the other for simulating inter-layer multi-scale boundaries in multi-layered graphite. The method is tested on benchmark nano-indentation problems and the results are consistent with the full domain solutions.