### 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 language | English |
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Title of host publication | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 |

Publication status | Published - 1 Dec 2000 |

Externally published | Yes |

Event | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 - Barcelona, Spain Duration: 11 Sep 2000 → 14 Sep 2000 |

### Conference

Conference | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 |
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Abbreviated title | ECCOMAS 2000 |

Country | Spain |

City | Barcelona |

Period | 11/09/00 → 14/09/00 |

### Fingerprint

### Keywords

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

### Cite this

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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - From discrete element simulations to a continuum model

AU - Luding, S.

AU - Lätzel, M.

AU - Volk, W.

AU - Diebels, S.

AU - Herrmann, H. J.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

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.

KW - Anisotropic materials

KW - Couette shear cell

KW - Fabric tensor

KW - MD simulation

KW - Micro-macro description

KW - Shear zone

KW - Stress- and strain-averaging

UR - http://www.scopus.com/inward/record.url?scp=84871167573&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9788489925700

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

ER -