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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