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Objective time derivatives revised

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Abstract

We propose a constructive introduction of the objective time derivatives based on the formulation of solid mechanics as a simple Lagrangian system. This enables to distinguish between deformation rates, which are in principle Lie derivatives, and stress rates, which are actually covariant derivatives along a curve representing a deformation process. Besides, the role of Daleckii–Krein formula in understanding the theory with generalized strains is highlighted, and a special attention will be paid to the logarithmic time derivative.

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Acknowledgements

The support through the Institutional Project RVO: 68378297 is gratefully acknowledged.

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  1. Institute of Theoretical and Applied Mechanics of the CAS, v. v. i., Prosecká 809/76, 190 00, Prague 9, Czech Republic

    Zdeněk Fiala

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Correspondence to Zdeněk Fiala.

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Fiala, Z. Objective time derivatives revised. Z. Angew. Math. Phys. 71, 4 (2020). https://doi.org/10.1007/s00033-019-1227-7

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  • DOI: https://doi.org/10.1007/s00033-019-1227-7

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