A concurrent multi-scale technique in modeling heterogeneous FCC nano-crystalline structures

•A multi-scale method is presented for heterogeneous nano-crystalline structures.•The multi-scale method is based on molecular dynamics–finite element coupling.•A Lagrange multiplier method is employed in the transition zone.•The stiffness and mass matrices of continuum domain are obtained from atomic zone.•The constraint equations of motion are solved by the multi-time-step technique.

In this paper, a multi-scale molecular dynamics–finite element coupling is presented to study the mechanical behavior of heterogeneous nano-crystalline structures. The stiffness and mass matrices of the continuum sub-domain are generated by applying a linear transformation on the matrices obtained via the atomic structure underlying the FE mesh. A Lagrange multiplier method is employed to the transition zone imposing velocity resemblance of the coupling regions. The constraint equations of motion are solved by the multi-time-step decomposition thus giving the opportunity to ascribe different time steps to each individual zone. The molecular dynamics is performed by employing the Sutton–RafiiTabar many body potential (Raffi-Tabar and Sutton, 1991) for FCC metallic alloys, and its integrity is attained by calculating the effective lattice parameter of different random alloys by minimizing the general form of Sutton–RafiiTabar interatomic potential energy. The authenticity and accuracy of the renovated concurrent scheme is remarkably acquired by comparing some numerical results of the proposed multi-scale model to those of implemented and validated molecular dynamics.