Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

References [Enhancements On Off] (What's this?)

  • [1] R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. & Anal. (in the press)
  • [2] S. Zaremba, Sur une conception nouvelle des forces intérieures dans un fluide en mouvement. Mém. Sci. Math. No. 82, Gauthier-Villars, Paris, 1937
  • [3] J. G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc. London. Ser. A. 200 (1950), 523–541. MR 0035192, https://doi.org/10.1098/rspa.1950.0035

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DOI: https://doi.org/10.1090/qam/69700
Article copyright: © Copyright 1955 American Mathematical Society

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