On response spectra and Kramers-Kronig relations in superposition rheometry

Abstract

In a recent paper, we derived expressions for determining the rate-dependent response spectra directly from parallel superposition rheometry data for the case of a certain Lodge-type integral constitutive model. It was shown that, within the confines of linear Yamamoto perturbation theory, the corresponding parallel superposition moduli satisfy the classical Kramers-Kronig relations. Special bases were presented to convert parallel superposition moduli to orthogonal superposition moduli. In the current paper, we obtain similar results for the integral models of Wagner I and, more generally, K-BKZ. These results facilitate the physical interpretation of parallel superposition moduli and direct model-based comparison of parallel and orthogonal superposition moduli in the study of weak nonlinear response.