Objective time derivatives

Note a constructive introduction of the objective time derivatives based on the formulation of solid mechanics as a simple Lagrangian system in [1]. 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 is also paid to the logarithmic time derivative.

[1] Fiala, Z.: Objective time derivatives revised. ZAMP 71, Article number: 4 (2020)