From discrete element simulations to a continuum model

S. Luding, M. Lätzel, W. Volk, S. Diebels, H. J. Herrmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)

Abstract

One of the essential questions in material sciences and especially in the area of granular matter is, how to obtain macroscopic quantities like velocity-field, stress or strain from "microscopic" quantities like contact-forces and -deformations as well as particle-displacements and rotations in a granular assembly. We examine a two-dimensional shear-cell by means of discrete element simulations and compute kinematic quantities like the velocity field, the elastic deformation gradient and the deformation rate. Furthermore, we examine the density, the coordination number, the fabric and the stress. From some combinations of those quantities, one gets e.g. The bulk-stiffness of the granulate and its shear modulus. The bulk modulus is a linear function of the trace of the fabric tensor which itself is proportional to the density and the coordination number. Finally, we note that the fabric, the stress and the strain tensors are not co-linear so that a more refined analysis than classical isotropic elasticity theory is required here. Another result is that the displacement rate (velocity) in the shear zone decays exponentially with the distance from the moving wall which applies the shear. Connected to the shear deformation is a rotation of the innermost layers in opposite direction, i.e. these layers roll over each other.

Original languageEnglish
Title of host publicationEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
Publication statusPublished - 1 Dec 2000
Externally publishedYes
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 - Barcelona, Spain
Duration: 11 Sep 200014 Sep 2000

Conference

ConferenceEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
Abbreviated titleECCOMAS 2000
CountrySpain
CityBarcelona
Period11/09/0014/09/00

Fingerprint

Discrete Elements
Continuum Model
Tensors
Elastic moduli
Velocity Field
Simulation
Tensor
Elastic deformation
Granular Matter
Materials science
Shear deformation
Bulk Modulus
Materials Science
Elastic Deformation
Contact Force
Elasticity
Elasticity Theory
Shear Deformation
Kinematics
Stiffness

Keywords

  • Anisotropic materials
  • Couette shear cell
  • Fabric tensor
  • MD simulation
  • Micro-macro description
  • Shear zone
  • Stress- and strain-averaging

Cite this

Luding, S., Lätzel, M., Volk, W., Diebels, S., & Herrmann, H. J. (2000). From discrete element simulations to a continuum model. In European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
Luding, S. ; Lätzel, M. ; Volk, W. ; Diebels, S. ; Herrmann, H. J. / From discrete element simulations to a continuum model. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000. 2000.
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Luding, S, Lätzel, M, Volk, W, Diebels, S & Herrmann, HJ 2000, From discrete element simulations to a continuum model. in European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, Spain, 11/09/00.

From discrete element simulations to a continuum model. / Luding, S.; Lätzel, M.; Volk, W.; Diebels, S.; Herrmann, H. J.

European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000. 2000.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - One of the essential questions in material sciences and especially in the area of granular matter is, how to obtain macroscopic quantities like velocity-field, stress or strain from "microscopic" quantities like contact-forces and -deformations as well as particle-displacements and rotations in a granular assembly. We examine a two-dimensional shear-cell by means of discrete element simulations and compute kinematic quantities like the velocity field, the elastic deformation gradient and the deformation rate. Furthermore, we examine the density, the coordination number, the fabric and the stress. From some combinations of those quantities, one gets e.g. The bulk-stiffness of the granulate and its shear modulus. The bulk modulus is a linear function of the trace of the fabric tensor which itself is proportional to the density and the coordination number. Finally, we note that the fabric, the stress and the strain tensors are not co-linear so that a more refined analysis than classical isotropic elasticity theory is required here. Another result is that the displacement rate (velocity) in the shear zone decays exponentially with the distance from the moving wall which applies the shear. Connected to the shear deformation is a rotation of the innermost layers in opposite direction, i.e. these layers roll over each other.

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Luding S, Lätzel M, Volk W, Diebels S, Herrmann HJ. From discrete element simulations to a continuum model. In European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000. 2000