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Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates. (English) Zbl 0984.74004
The authors consider the long-standing problem of the choice of objective time rate of symmetric Eulerian tensors in continuum mechanics. The most well-known proposals are those made by Zaremba and Jaumann, Oldroyd, Naghdi and Wainright – and the general notion of Lie derivative. Here, accounting for the fact that the objectivity is not the only requirement, but identification with the deformation rate may be a useful constraint, the authors show the need to use corotational rates. It is finally proved that only Hencky strain can have an objective corotational rate. The spin involved then is the logarithmic spin as defined in a former paper [H. Xiao, O. T. Bruhns and A. Meyers, Acta Mech. 124, No. 1-4, 89-105 (1997; Zbl 0909.73006)].
Reviewer: G.A.Maugin (Paris)

74A05 Kinematics of deformation
74A20 Theory of constitutive functions in solid mechanics
Full Text: DOI
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