Abstract
It is shown that if a motion is such that the first two Rivlin-Ericksen tensors A 1 and A 2 have the same unit proper vectors, and A1 has distinct proper numbers, then all the Rivlin-Ericksen tensors A 1, A 2, ..., A n, ... have the same proper vectors. If further this motion is steady and isochoric, then the product of velocity components corresponding to the unit proper vectors, assumed to be non-vanishing, and the product of the abnormalities of the vector fields of the proper vectors, also assumed to be non-vanishing, each bear a constant value along a streamline. If A 1 has a pair of equal proper numbers the first statement remains true, but the results for steady isochoric motions will not necessarily hold.
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References
1970 A. W. Marris & C.-C. Wang, “Solenoidal Screw Fields of Constant Magnitude”, Arch. Rational Mech. Anal., Vol. 39, No. 3, 227–244.
1979 A. W. Marris, “Steady Universal Motions of Rivlin-Ericksen Fluids”, Arch. Rational Mech. Anal, Vol. 69, No. 4, 335–380.
1989 A. W. Marris, “Steady Circulation-Preserving Motions with Certain Conditions on the Rivlin-Ericksen Tensors A 1 and A 2, Arch. Rational Mech. Anal., Vol. 106, No. 3, 195–209.
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Communicated by K. R. rajagopal
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Marris, A.W. A property of the set of Rivlin-Ericksen tensors. Arch. Rational Mech. Anal. 111, 197–209 (1990). https://doi.org/10.1007/BF00400109
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DOI: https://doi.org/10.1007/BF00400109