A Concurrent Multiscale Micromorphic Molecular Dynamics. Part I. Theoretical Formulation
Based on a novel concept of multiplicative multiscale decomposition, we have derived a multiscale micromorphic molecular dynamics (MMMD)to extent the (Andersen)-Parrinello-Rahman molecular dynamics to mesoscale and macroscale. The multiscale micromorphic molecular dynamics is a con-current three-scale particle dynamics that couples a fine scale molecular dynamics, a mesoscale particle dynamics of micromorphic medium, and a coarse scale nonlocal particle dynamics of nonlinear continuum. By choosing proper statistical closure conditions, we have shown that the original Andersen-Parrinello-Rahman molecular dynamics can be rigorously formulated and justified from first principle, and it is a special case of the proposed multiscale micromorphic molecular dynamics. The discovered mutiscale structure and the corresponding multiscale dynamics reveal a seamless transition channel from atomistic scale to continuum scale and the intrinsic coupling relation among them, and it can be used to solve finite size nanoscale science and engineering problems with arbitrary boundary conditions.