Modeling the strain dependence of torque harmonics as measured through large-amplitude oscillatory shear rheometry

Data describing the stress response to large‐amplitude oscillatory shear can be considered as the nonlinear viscoelastic signature of polymer materials. How such data can be fitted with an appropriate equation is a problem of prime importance because (1) it allows results gathered in a large strain window to be summarized in a small number of representative parameters and (2) it permits a physical significance to be sought for equation parameters. This article analyzes and discusses several mathematical relationships that were proposed in the literature to fit harmonics vs. strain data, and probes their relative merits with various sets of experimental results. A simple four‐parameter model is shown to encompass all the other approaches and to yield parameters that correctly describe not only material behavior in the linear‐to‐nonlinear transition region but also in the asymptotic high‐strain range. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012