Summary: manuscript No.
(will be inserted by the editor)
From discrete particles to continuum fields near a boundary
Thomas Weinhart1,2, · Anthony R. Thornton1,2 · Stefan Luding1 · Onno Bokhove2
Deadlines: Submission of manuscript - August 1, 2011 (extended), Review - September 1, 2011, 6 pages max.
Abstract An expression for the stress tensor near an exter-
nal boundary of a discrete mechanical system is derived ex-
plicitly in terms of the constituents' degrees of freedom and
interaction forces. Starting point is the exact and general
coarse graining formulation presented by Goldhirsch in [I.
Goldhirsch, Gran. Mat., 12(3):239-252,2010], which is con-
sistent with the continuum equations everywhere but does
not account for boundaries. Our extension accounts for the
boundary interaction forces in a self-consistent way and thus
allows the construction of continuous stress fields that obey
the macroscopic conservation laws even within one coarse-
graining width of the boundary.
The resolution and shape of the coarse-graining function
used in the formulation can be chosen freely, such that both
microscopic and macroscopic effects can be studied. The