Abstract <p>We measure the rheological properties of a newly formulated silicone-based ink for additive manufacturing technologies. The basic measurement for such viscoelastic non-Newtonian fluids, namely small amplitude oscillatory shear (SAOS) highlights the need to consider a relaxation time of the polymeric microstructure that depends smoothly on the oscillation frequency. We incorporate this information within a recently developed framework for the tensorial description of viscoealastic fluids. With this, we can achieve a significant improvement in the fitting of the experimental data. Moreover, we can extrapolate the frequency dependence of the relaxation time to its rate dependence in steady shear flows, leading to a prediction of both the viscosity and the first normal stress coefficient which is in good agreement with experiments. This provides a new way to connect the linear viscoelastic response to the nonlinear response of the material.</p> Graphical Abstract <p></p>