### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 6 |

Publication status | Published - Aug 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | Department 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

*From discrete particles to continuum fields near a boundary*. (Memorandum / Department of Applied Mathematics; No. 1950). Enschede: University of Twente, Department of Applied Mathematics.

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*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.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - From discrete particles to continuum fields near a boundary

AU - Weinhart, Thomas

AU - Thornton, Anthony Richard

AU - Luding, Stefan

AU - Bokhove, Onno

PY - 2011/8

Y1 - 2011/8

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

KW - Stress

KW - Continuum mechanics

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - From discrete particles to continuum fields near a boundary

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -