From discrete particles to continuum fields near a boundary

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Abstract

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 in [I.Goldhirsch, Gran.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 and steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (highly rough) boundaries. Two discrete particle method (DPM) simulations are presented in which the novel boundary treatment is exemplified, including a chute flow over a base with roughness greater than a particle diameter.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages6
Publication statusPublished - Aug 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherDepartment of Applied Mathematics, University of Twente
No.1950
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • EWI-20426
  • DPM (DEM)
  • IR-77931
  • Granular systems
  • Averaging
  • Coarse Graining
  • Discrete mechanical systems
  • Homogenisation
  • Boundary treatment
  • METIS-279720
  • Stress
  • Continuum mechanics

Cite this

Weinhart, T., Thornton, A. R., Luding, S., & Bokhove, O. (2011). From discrete particles to continuum fields near a boundary. (Memorandum / Department of Applied Mathematics; No. 1950). Enschede: University of Twente, Department of Applied Mathematics.
Weinhart, Thomas ; Thornton, Anthony Richard ; Luding, Stefan ; Bokhove, Onno. / From discrete particles to continuum fields near a boundary. Enschede : University of Twente, Department of Applied Mathematics, 2011. 6 p. (Memorandum / Department of Applied Mathematics; 1950).
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abstract = "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 in [I.Goldhirsch, Gran.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 and steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (highly rough) boundaries. Two discrete particle method (DPM) simulations are presented in which the novel boundary treatment is exemplified, including a chute flow over a base with roughness greater than a particle diameter.",
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author = "Thomas Weinhart and Thornton, {Anthony Richard} and Stefan Luding and Onno Bokhove",
year = "2011",
month = "8",
language = "Undefined",
series = "Memorandum / Department of Applied Mathematics",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1950",

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Weinhart, T, Thornton, AR, Luding, S & Bokhove, O 2011, From discrete particles to continuum fields near a boundary. Memorandum / Department of Applied Mathematics, no. 1950, University of Twente, Department of Applied Mathematics, Enschede.

From discrete particles to continuum fields near a boundary. / Weinhart, Thomas; Thornton, Anthony Richard; Luding, Stefan; Bokhove, Onno.

Enschede : University of Twente, Department of Applied Mathematics, 2011. 6 p. (Memorandum / Department of Applied Mathematics; No. 1950).

Research output: Book/ReportReportProfessional

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AU - Luding, Stefan

AU - Bokhove, Onno

PY - 2011/8

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N2 - 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 in [I.Goldhirsch, Gran.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 and steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (highly rough) boundaries. Two discrete particle method (DPM) simulations are presented in which the novel boundary treatment is exemplified, including a chute flow over a base with roughness greater than a particle diameter.

AB - 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 in [I.Goldhirsch, Gran.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 and steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (highly rough) boundaries. Two discrete particle method (DPM) simulations are presented in which the novel boundary treatment is exemplified, including a chute flow over a base with roughness greater than a particle diameter.

KW - EWI-20426

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KW - METIS-279720

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Weinhart T, Thornton AR, Luding S, Bokhove O. From discrete particles to continuum fields near a boundary. Enschede: University of Twente, Department of Applied Mathematics, 2011. 6 p. (Memorandum / Department of Applied Mathematics; 1950).