The unification of disparate rheological measures in oscillatory shearing

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments.