Generalized bridging domain method for coupling finite elements with discrete elements

Fubin Tu, Daosheng Ling, Lingfang Bu, Qingda Yang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The concurrent coupling of finite elements and discrete elements is an effective DOF reduction methodology for reproducing the granular flow phenomenon as discrete element method does. In this paper, we present a novel coupling strategy named the generalized bridging domain method. This method introduces independent functions to weight the material properties of the continuum and those of the discrete element model, and then the equilibrium of each new model is guaranteed by imposing compensation forces. The compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements, and vice versa. Utilizing different weighting functions, four typical coupling methods, the bridging domain method, edge-to-edge coupling, separate domain coupling, and separate edge coupling, are obtained. Additionally, a new integration algorithm with multiple time steps is developed for the separate edge coupling. The numerical performance of the separate domain coupling, where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the Lagrange multiplier method, has been investigated in detail. Results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements. Due to the truncation of high frequency waves, there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model.

Original languageEnglish
Pages (from-to)509-533
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Volume276
DOIs
StatePublished - Jul 1 2014

Fingerprint

Lagrange multipliers
Finite difference method
Energy dissipation
Materials properties
continuums
compatibility
weighting functions
Compensation and Redress
energy dissipation
methodology
requirements
approximation

Keywords

  • Discrete element method
  • Finite element method
  • Granular flow phenomenon
  • Multiscale method
  • Spurious wave reflection

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

Generalized bridging domain method for coupling finite elements with discrete elements. / Tu, Fubin; Ling, Daosheng; Bu, Lingfang; Yang, Qingda.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 276, 01.07.2014, p. 509-533.

Research output: Contribution to journalArticle

@article{51bbb3af9564487fb5b7bbc1ff7c91af,
title = "Generalized bridging domain method for coupling finite elements with discrete elements",
abstract = "The concurrent coupling of finite elements and discrete elements is an effective DOF reduction methodology for reproducing the granular flow phenomenon as discrete element method does. In this paper, we present a novel coupling strategy named the generalized bridging domain method. This method introduces independent functions to weight the material properties of the continuum and those of the discrete element model, and then the equilibrium of each new model is guaranteed by imposing compensation forces. The compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements, and vice versa. Utilizing different weighting functions, four typical coupling methods, the bridging domain method, edge-to-edge coupling, separate domain coupling, and separate edge coupling, are obtained. Additionally, a new integration algorithm with multiple time steps is developed for the separate edge coupling. The numerical performance of the separate domain coupling, where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the Lagrange multiplier method, has been investigated in detail. Results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements. Due to the truncation of high frequency waves, there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model.",
keywords = "Discrete element method, Finite element method, Granular flow phenomenon, Multiscale method, Spurious wave reflection",
author = "Fubin Tu and Daosheng Ling and Lingfang Bu and Qingda Yang",
year = "2014",
month = "7",
day = "1",
doi = "10.1016/j.cma.2014.03.023",
language = "English",
volume = "276",
pages = "509--533",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0374-2830",
publisher = "Elsevier",

}

TY - JOUR

T1 - Generalized bridging domain method for coupling finite elements with discrete elements

AU - Tu, Fubin

AU - Ling, Daosheng

AU - Bu, Lingfang

AU - Yang, Qingda

PY - 2014/7/1

Y1 - 2014/7/1

N2 - The concurrent coupling of finite elements and discrete elements is an effective DOF reduction methodology for reproducing the granular flow phenomenon as discrete element method does. In this paper, we present a novel coupling strategy named the generalized bridging domain method. This method introduces independent functions to weight the material properties of the continuum and those of the discrete element model, and then the equilibrium of each new model is guaranteed by imposing compensation forces. The compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements, and vice versa. Utilizing different weighting functions, four typical coupling methods, the bridging domain method, edge-to-edge coupling, separate domain coupling, and separate edge coupling, are obtained. Additionally, a new integration algorithm with multiple time steps is developed for the separate edge coupling. The numerical performance of the separate domain coupling, where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the Lagrange multiplier method, has been investigated in detail. Results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements. Due to the truncation of high frequency waves, there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model.

AB - The concurrent coupling of finite elements and discrete elements is an effective DOF reduction methodology for reproducing the granular flow phenomenon as discrete element method does. In this paper, we present a novel coupling strategy named the generalized bridging domain method. This method introduces independent functions to weight the material properties of the continuum and those of the discrete element model, and then the equilibrium of each new model is guaranteed by imposing compensation forces. The compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements, and vice versa. Utilizing different weighting functions, four typical coupling methods, the bridging domain method, edge-to-edge coupling, separate domain coupling, and separate edge coupling, are obtained. Additionally, a new integration algorithm with multiple time steps is developed for the separate edge coupling. The numerical performance of the separate domain coupling, where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the Lagrange multiplier method, has been investigated in detail. Results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements. Due to the truncation of high frequency waves, there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model.

KW - Discrete element method

KW - Finite element method

KW - Granular flow phenomenon

KW - Multiscale method

KW - Spurious wave reflection

UR - http://www.scopus.com/inward/record.url?scp=84899880837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899880837&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2014.03.023

DO - 10.1016/j.cma.2014.03.023

M3 - Article

VL - 276

SP - 509

EP - 533

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -