Tensors associated with time-dependent stress
Authors:
Barbara A. Cotter and R. S. Rivlin
Journal:
Quart. Appl. Math. 13 (1955), 177-182
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/69700
MathSciNet review:
69700
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Abstract: It is assumed that six functional relations exist between the components of stress and their first $m$ material time derivatives and the gradients of displacement, velocity, acceleration, second acceleration, . . . , $\left ( {n - 1} \right )$th acceleration. It is shown that these relations may then be expressed as relations between the components of $m + n + 2$ symmetric tensors if $n \> m$, and $2m + 2$ symmetric tensors if $m \> n$. Expressions for these tensors are obtained.
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. & Anal. (in the press)
S. Zaremba, Sur une conception nouvelle des forces intérieures dans un fluide en mouvement. Mém. Sci. Math. No. 82, Gauthier-Villars, Paris, 1937
- J. G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc. London Ser. A 200 (1950), 523–541. MR 35192, DOI https://doi.org/10.1098/rspa.1950.0035
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. & Anal. (in the press)
S. Zaremba, Sur une conception nouvelle des forces intérieures dans un fluide en mouvement. Mém. Sci. Math. No. 82, Gauthier-Villars, Paris, 1937
J. G. Oldroyd, On the formulation of rheological equations of state. Proc. Roy. Soc. A200, 523 (1950)
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Article copyright:
© Copyright 1955
American Mathematical Society
