Abstract
As mentioned in Section 1.6, a powder at rest constitutes a mechanical structure. This means that it can withstand certain stresses applied from the outside without permanent distortion, so that it returns to its original configuration when the stresses are relieved. Thus the powder structure is elastic within certain limits, and inside the powder structure stresses are generated that compensate for the outward stresses. When the elasticity limits are exceeded a plastic deformation results from which the powder will not return to its original configuration. At any point in the powder the stress situation is described by the stress tensor σ. From point to point this stress tensor may vary but only continuously.
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Abbreviations
- A:
-
pg + dp/dy (see eqn (3.31)) (N m -3)
- Dc :
-
Maximum diameter of free arch (m)
- H:
-
Bed height (m)
- I1, I2, I3 :
-
Invariants (see eqn (3.16)) (N m -2)
- l, m, n:
-
Direction cosines (—)
- p:
-
Gas pressure in fluidization (N m -2)
- P:
-
Stress on a plane through O (N m -2)
- Pd :
-
Isotropic pressure in powder mass (N m -2)
- q:
-
Stress with components qx qyand qz(N m -2)
- r:
-
Radius of Mohr circles
- ra :
-
Radius of critical Mohr circle (N m -2)
- R:
-
Bed radius (m)
- vco :
-
Superficial gas flow rate (m s -1)
- ε:
-
Porosity of powder bed (—)
- ß:
-
Slope of heap of powder (—)
- θ:
-
Angle between principal axis and x-direction (—)
- ρ:
-
Average bulk density of powder (kg m -3)
- σc :
-
Tension cutoff (N m -2)
- σ:
-
Powder stress tensor (N m -2)
- σ1, σ2, σ3 :
-
Principal stresses (N m -2)
- τ:
-
Shear stress (N m -2)
- τ0 :
-
Cohesion constant (N m -2)
- ø:
-
Angle of internal friction (—)
References
Jaeger, J.C. (1969). Elasticity, Fracture and Flow. Science Paperbacks, Methuen, London.
Roscoe, K.H. (1967). Behandlung bodenmechanischer Probleme auf der Grundlage neuerer Forschungsergebnisse Bergbauwissenschaften, 14, 464.
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© 1991 Elsevier Science Publishers Ltd
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Rietema, K. (1991). Mechanics of Powders at Rest. In: The Dynamics of Fine Powders. Elsevier Handling and Processing of Solids Series. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3672-3_3
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DOI: https://doi.org/10.1007/978-94-011-3672-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-594-5
Online ISBN: 978-94-011-3672-3
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