An atomistic-to-continuum molecular dynamics: Theory, algorithm, and applications

To study the connection between atomistic molecular dynamics and macroscale continuum mechanics, we partition the Lagrangian of first-principle molecular dynamics according to its length scales. By doing so, we discover a universal three-scale structure that is embedded in the conventional molecular dynamics formulation, which provides an intrinsic and seamless transition from microscale to macroscale. The multiscale micromorphic molecular dynamics (MMMD) is built on a novel micromorphic multiplicative decomposition that couples a fine scale atomistic dynamics, a mesoscale micromorphic dynamics, and a macroscale particle dynamics of continuum mechanics together in concurrent fashion. In this work, we discuss the relationship between MMMD and nonlinear continuum mechanics, its computational algorithm, and how to use it to simulate phase transformation under non-equilibrium conditions.