From discrete particles to continuum fields near a boundary

An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch (Granul Mat 12(3):2...

Full description

Saved in:
Bibliographic Details
Published in:Granular matter 2012-04, Vol.14 (2), p.289-294
Main Authors: Weinhart, Thomas, Thornton, Anthony R., Luding, Stefan, Bokhove, Onno
Format: Article
Language:English
Subjects:
Complex Fluids and Microfluidics
Engineering Fluid Dynamics
Engineering Thermodynamics
Foundations
Geoengineering
Heat and Mass Transfer
Hydraulics
Industrial Chemistry/Chemical Engineering
Materials Science
Mechanics
Original Paper
Physics
Physics and Astronomy
Soft and Granular Matter
Stress analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch (Granul Mat 12(3):239–252, 2010 ), which is consistent 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 method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static or steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (very rough) boundaries. Discrete particle simulations are presented in which the novel boundary treatment is exemplified, including chute flow over a base with roughness greater than one particle diameter.
ISSN:1434-5021
1434-7636
DOI:10.1007/s10035-012-0317-4