On the formulation of rheological equations of state
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Tài liệu tham khảo
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Frdhlich H., 1946, Proc. Roy, Soc. A, 185, 415
Hencky H. 1925 Z.angew. Math. Mech.
Jeffreys H. 1931 Cartesian tensors chap. vm . Cambridge University Press.
Mumaghan F. D., 1937, Amer, J. Math., 59, 235
Rivlin R. S., 1948, Proc. Roy, Soc. A, 193, 260
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various liquids and has been attributed by him to a combination of viscous and elastic
properties giving rise to a tensile stress in the direction of the streamlines (<?><£'>0 as in
material B). [Note added 29 October 1949.] Reiner (1948 1949) regards the effect observed by Weissenberg
as a manifestation of cross-elasticity a term used of materials in which a single applied shear
stress gives rise to elastic strains in all directions. On the other hand Rivlin (1948) has shown
in detail how the same phenomenon could arise in a non-Newtonian viscous liquid exhibiting
no elasticity but is mistaken in suggesting that elastic properties could not be a contributory
cause. (His argument is that the 'time derivatives of the stress components *which occur in the
equations of state of an elastic liquid vanish in a steady state of flow so that the equations of
state are then indistinguishable from those of an inelastic liquid. In fact the simplest equations
of state representing elastico-viscous behaviour must be expressible as equations relating the
rate-of-strain tensor the stress tensor and the convected derivative of the stress tensor.
In a steady state partial time derivatives in an Eulerian system of reference vanish but the
convected derivative of the stress tensor does not vanish and does not reduce to an algebraic
combination of the stress and rate-of-strain tensors. Therefore an elastico-viscous liquid will in
general behave differently from any inelastic viscous liquid even in steady-state experiments.)