| A distinction between molecular dynamics (MD) and classical continuum
mechanics (CM) is that the former assumes a nonlocal model of force
interaction. This distinction complicates any practical scheme for
coarse-graining MD into classical CM, for instance when the finite
element method is used for the classical CM discretization. This paper
describes a method for representing a collection of atoms at finite
temperature as a peridynamic (PD) body. In direct analogy with MD, PD, a
continuum theory, uses a nonlocal model of force and avoids the notion
of strain germane
to classical CM. The PD representation is then homogenized and rescaled
to enable a statistical coarse-graining of MD. The coarse-graining
avoids the use of a unit cell and the Cauchy-Born rule. In contrast with
classical CM, the PD homogenized system of linear springs and masses is
shown to have the same dispersion relation as the original spring-mass
system. A non-local notion of PD stress is also presented. |
