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 |
|---|---|
| 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 |
|---|---|
| Abbreviated title | ECCOMAS 2000 |
| Country | Spain |
| City | Barcelona |
| Period | 11/09/00 → 14/09/00 |
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Keywords
- Anisotropic materials
- Couette shear cell
- Fabric tensor
- MD simulation
- Micro-macro description
- Shear zone
- Stress- and strain-averaging
Cite this
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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 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 -