Abstract
In this paper the restrictions of the so-called chain rule on objective time-derivatives are examined. A generalization of the chain rule on scalar valued isotropic tensor functions with more than one tensorial arguments (second order tensors) is also introduced. The analysis shows that there are different solutions associated with the chain rule. Not all of them have a physical significance. With respect to the physical reasonable solutions and a so-called invariance condition the chain rule gives an additional restriction if different objective time-derivatives for different arguments in scalar isotropic tensor functions are used. In such a situation the antimetric part of the tensor of convective velocity has to be the same in each objective time-derivative.
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