Useful Conservation Sums in Molecular Dynamics and Atomistics

Abstract

Configuration forces of an arbitrary molecular dynamics domain are derived in which the energetic characteristics are approximated as those of a non-local gradient elastic field. The configuration forces include not only the effects of the strain gradients but also those of micro-polar energetics. The useful sums represent approximate expressions of translational, expansional and rotational configuration forces. Particular homogenization of the field makes the continuum limits of the sums approximately obey configurational transformation symmetries to satisfy Noether’s theorem, and to converge to generalized J integral for static non-local elastic fields of homogeneous media; however, the non-local M and L integrals do not have corresponding conservation laws. Interpolation and projection schemes of a molecular dynamics or atomistics system onto a system of continuum motions and energetics are also derived for elastic as well as non-elastic cases.