From molecular systems to continuum solids: A multiscale structure and dynamics.

Abstract

We propose a concurrent multiscale molecular dynamics for molecular systems in order to apply macroscale mechanical boundary conditions such as traction and average displacement for solid state materials, which is difficult to do in traditional molecular dynamics where boundary conditions are applied in terms of forces and displacements on selected particles. The multiscale model is systematically constructed in terms of multiscale structures of kinematics, force field, and dynamical equations. The idea is to extend the Anderson-Parrinello-Rahman molecular dynamics to the cases that have arbitrary finite domain and boundary, thus the model is capable of solving inhomogeneous, non-equilibrium problems. The macroscale stress loading on a representative volume element with periodic boundary condition is generalized to all kinds of macroscale mechanical boundary conditions. Unlike most multiscale techniques, our theory is aimed at understanding fundamental physics rather than achieving computing efficiency. Examples of problems with prescribed average displacements and surface tractions are presented to demonstrate the validity of the proposed multiscale molecular dynamics.