A concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

In this paper, a new multi-scale technique is developed for concurrent coupling of atomistic-continuum domains in modeling nano-mechanical behavior of atomic structures. A Lagrange multiplier method is employed over an overlapping domain to coupling the continuum nodal velocities with atomic lattice velocities. The Hamiltonian method is applied to combine the continuum and molecular Hamiltonians with the same weight in the overlapping domain. The mass and stiffness matrices of the continuum domain are obtained using a linear bridging map of the atomic lattice displacement laid underneath the continuum grid to the element displacements. Numerical examples are performed by presenting the stress and displacement distributions over the continuum and molecular domains in both coupling and molecular dynamic methods where a good agreement is perceived. A comparison of two methods at the surface, demonstrates the capability of the coupling method to practically consider the surface effects. Also, an illustration of energy distribution along the time and domain approves the capability of the represented method to thoroughly eliminate the spurious wave reflection at the atomic-continuum interface.