Reformulation of microscopic balance equations for multiscale materials modeling

In this paper we present a new formalism that analytically links atomic variables to continuously distributed local properties and that leads to a concurrent two-level representation of balance laws for atomistic systems with general lattice structure. The new component of this formulation is an explicit decomposition of associated fluxes in multiatomic lattices into components representing the distortions of lattice cells and the rearrangement of atoms within the lattice cells. New formulation of balance laws is obtained in a form that is suitable for a direct atomistic analysis at fine scale to a continuum analysis in coarse scales. The results of this work will provide a new continuum field representation of classical N-body dynamics that can fully reproduce phonon dispersion relations of multiatomic crystalline materials and will enable coupled atomistic and continuum simulations within a single theoretical framework.