From the summary: We present a constitutive equation for non-Newtonian materials which is capable of predicting, independently, steady state rheological material functions both in shear and in extension. The basic assumption is that the extra-stress tensor is a function of both the rate-of-strain tensor, \(\mathbf D\), and the persistence-of-straining tensor, \(\mathbf P=\mathbf D\overline{\mathbf W}-\overline{\mathbf W}\mathbf D\). The resulting equation falls within the category of constitutive equations of the form \(\boldsymbol \tau=\boldsymbol \tau(\mathbf D,\overline{\mathbf W})\), with the advantage of eliminating the undesirable stress jumps that may occur when \(\overline {\mathbf W}\) becomes locally undetermined. We also show that this formulation is not restricted to motions with constant relative principle stretch history (MWCRPSH), in contrast to what is suggested in the literature. The same basis of tensors that comes from representation theorems also arises from an elastic constitutive equation based on the difference between the Jauman and the Harnoy convected time derivatives, in the limit of small values of the Deborah number.