A coupling atomistic–continuum approach for modeling mechanical behavior of nano-crystalline structures

In this article, a novel approach is presented for the concurrent coupling of continuum–atomistic model in the nano-mechanical behavior of atomic structures. The study is focused on the static concurrent multi-scale simulation, which is able to effectively capture the surface effects intrinsic in the molecular mechanics modeling. The Hamiltonian approach is applied to combine the continuum and molecular models with the same weight in the overlapping domain. A Lagrange-multiplier method is employed over the overlapping domain for coupling the continuum nodal displacement with the atomic lattice deformation. A multiple-step algorithm is developed to decouple the solution process in the atomic and continuum domains. The mass and stiffness matrices of continuum domain are computed based on the linear bridging map of the atomic lattice displacement, laid underneath the continuum grid to the element displacements. Numerical simulation results present that the stress and displacement contours of the presented coupling method are in good agreement with those obtained from the molecular mechanics simulation.