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).
    @book{db634b2b3590402ba11f8935c86feb9e,
    title = "From discrete particles to continuum fields near a boundary",
    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.",
    keywords = "EWI-20426, DPM (DEM), IR-77931, Granular systems, Averaging, Coarse Graining, Discrete mechanical systems, Homogenisation, Boundary treatment, METIS-279720, Stress, Continuum mechanics",
    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",

    }

    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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    T1 - From discrete particles to continuum fields near a boundary

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    AU - Thornton, Anthony Richard

    AU - Luding, Stefan

    AU - Bokhove, Onno

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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

    KW - DPM (DEM)

    KW - IR-77931

    KW - Granular systems

    KW - Averaging

    KW - Coarse Graining

    KW - Discrete mechanical systems

    KW - Homogenisation

    KW - Boundary treatment

    KW - METIS-279720

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    KW - Continuum mechanics

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    PB - University of Twente, Department of Applied Mathematics

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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).