In this presentation, we shall introduce a con-current multiscale micromorphic molecular dynamics (MCMD), which generalizes the classical Andersen-Parrinello-Rahman molecular dynamics to inhomogeneous and non-equilibrium systems with arbitrary finite domains. More importantly, it can take into account the macroscale continuum boundary condition as the input of molecular dynamics.

The multiscale micromorphic molecular dynamics is a con-current coupling of the fine scale molecular dynamics with a coarse scale finite element based nonlinear mesoscale continuum dynamics. By choosing proper closure conditions, we have shown that the Andersen-Parrinello-Rahman molecular dynamics is a special case of the proposed multiscale molecular dynamics. In other words, we have shown that the Andersen-Parrinello-Rahman molecular dynamics can be rigorously formulated and justified from first principle. Moreover, we also show that one may be able to derive the basic equations of nonlinear mesoscale continuum mechanics from first principle.

Furthermore, the con-current multiscale continuum-molecular dynamics provides a solid foundation for general non-equilibrium molecular dynamics. To implement this con-current multiscale formalism, we have developed a three-dimensional multiscale continuum-molecular dynamics computer code, which couples the Parrinello-Rahman (PR) molecular dynamics with non-linear finite element based continuum dynamics. In this presentation, we shall present several numerical examples of the proposed MMMD to demonstrate the validity as well as the applications of the proposed multiscale method.