Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates

In recent years the role of a convenient objective rate of objective quanti ties has been passionately discussed. There is a large number of well-justi fied formulations, e.g., [8], [13], [16]. For an overview of some selected derivatives see, e.g., [21]. However, unreliable results obtained in specif ic computations [11] complicate the right choice. Moreover, from a physical point of view there exist some additional requirements on time derivatives besides the principle of objectivity [5]. In this paper we try to show tha t there is a need for using corotational rates. For that purpose we give di fferent approaches. In an application to the aforementioned facts we prove that only the Hencky strain [6] can have an objective corotational rate. We do that by identifying the objective strain rate and the deformation rate. Moreover, the spin involved in this rate is the logarithmic spin as define d in [23].