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A note on linear transversely isotropic fluids

Published online by Cambridge University Press:  26 February 2010

A. E. Green
Affiliation:
Department of Mathematics, The University of Newcastle upon Tyne

Extract

Green [8] has shown that a constitutive relation of the form

arises as a special case of an incompressible anisotropic simple fluid, where S is the stress tensor or matrix,

and V is the velocity gradient matrix at time t, all measured in a fixed rectangular cartesian coordinate system. Also, if F is the displacement gradient measured with respect to some curvilinear reference system θi, then

where R is a proper orthogonal matrix, and M and K are positive definite symmetric matrices. In addition

and

Type
Research Article
Copyright
Copyright © University College London 1965

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References

1. Ericksen, J. L., Kolloid Zeitschrift, 173 (1960), 117.CrossRefGoogle Scholar
2. Ericksen, J. L., Arch. Rational Mech. Anal., 4 (1960), 231.CrossRefGoogle Scholar
3. Ericksen, J. L., Trans. Soc. Rheology, 4 (1960), 29.CrossRefGoogle Scholar
4. Ericksen, J. L., Arch. Rational Mech. Anal., 8 (1961), 1.CrossRefGoogle Scholar
5. Ericksen, J. L., Trans. Soc. Rheology, 5 (1961), 23.CrossRefGoogle Scholar
6. Ericksen, J. L., Trans. Soc. Rheology, 6 (1962), 273.CrossRefGoogle Scholar
7. Green, A. E., Proc. Camb. Phil. Soc, 60 (1964), 123CrossRefGoogle Scholar
8. Ericksen, J. L., Proc. Roy. Soc., A 279 (1964), 437.Google Scholar
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