 
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):239252,2010], 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 selfconsistent 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 coarsegraining function
used in the formulation can be chosen freely, such that both
microscopic and macroscopic effects can be studied. The
