An enhanced bridging domain method for linking atomistic and continuum domains

• The performance of bridging domain method is numerically verified.
• A technique is developed to enhance the performance of bridging domain method.
• The total displacement field is decomposing into fine and coarse scale fields.
• The equations of motion of fine scale oscillations are derived.
• The fine scales are removed by inserting a damping term in their equations of motion.

Bridging domain method (BDM) is a multiscale method which couples molecular dynamics (MD) with finite element simulations. In this paper, using numerical study we show that time integration step size and the discretization of Lagrange multipliers can highly impact the capability of BDM in removing spurious reflections. We present a technique to enhance the performance of bridging domain method and to alleviate the effects of the two aforementioned factors on the BDM. In our technique, the total displacement field of the atoms located in the overlapping zone is decomposed into a coarse and a fine field. The equations of motion of fine scale oscillations are first obtained and then modified to include a damping term. The damping condition effectively filters out and removes the fine scale oscillations that cannot pass into the continuum domain; hence eliminates the spurious wave reflections. Using numerical examples, we show that the proposed enhancement significantly improves the performance of bridging domain method. This is specially significant when discontinuities such as cracks are present in the domain or when the integration time step is small.