Motions with zero acceleration and their relevance in viscoelasticity

It is shown that motions with zero acceleration in incompressible materials consist of velocity fields which are steady or unsteady in the Eulerian sense. Moreover, in these motions all Rivlin-Erickson tensors of order three and higher are zero. Consequently, it is shown that there are non-viscometric flows in which Rivlin-Ericksen tensors of order three and higher are all zero. An example of a homogeneous motion with an unsteady velocity field is given to highlight this fact and a general method to generate such flows, which may be non-homogeneous, is also indicated.