Objective rate equations and memory properties in continuum physics

The paper deals with the modelling of material behaviours in continuum physics by means of rate equations. The research has a twofold purpose. First, to review the structure of objective time derivatives, namely invariant derivatives within the set of Euclidean transformations; known derivatives occurring in the literature are shown to be particular cases of the whole family of objective time derivatives. Second, to investigate the thermodynamic consistency of some models involving objective time derivatives. In particular, two topics are developed. One is the improvement of the constitutive equation of viscous fluids. The other topic is a possible rate equation for the stress. The thermodynamic consistency is shown in connection with the co-rotational derivative.