Connecting molecular dynamics to micromorphic theory. (II). Balance laws

In this paper, the time evolution laws for the averaged conserved dynamical variables are derived based on a molecular dynamic model. It is found that they follow exactly the balance laws in micromorphic continuum, derived by Eringen in a top-down approach. Since all the mechanical variables in micromorphic theory can be obtained from an atomic model through statistical ensemble averaging, and those averaged quantities satisfy the balance laws that govern the behavior of the continuum, it is thus concluded that the atomic model is consistent with the continuum model, and correspondence between these two models is analytically achieved.