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Two-dimensional plastic flow of a Bingham solid

A plastic boundary-layer theory for slow motion

Published online by Cambridge University Press:  24 October 2008

J. G. Oldroyd
J. G. Oldroyd
Affiliation:
Courtaulds, Ltd Research LaboratoryMaidenhead, Berks.
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Extract

The rheological equations of state for an isotropic Bingham solid may be written in tensor form:

where

The notation is explained fully in a previous paper (1). The frame of reference is essentially Eulerian. Primes denote deviatoric components of the stress, strain and rate of strain tensors, pik, εik and eik (for example, ). The dilatation is denoted by Δ. The rigidity and bulk moduli μ and κ are, if not constants, essentially scalar functions of the stress tensor. The variable viscosity η involves two constants, the yield value ϑ and the reciprocal mobility η1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 3 , July 1947 , pp. 383 - 395
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

REFERENCES

(1)Oldroyd, J. G.Proc. Cambridge Phil. Soc. 43 (1947), 100.Google Scholar
(2)Blasius, H. Z.Math. Phys. 56 (1908), 1.Google Scholar