Unified interpretation of MAOS responses via experimentally decomposed material functions

Oscillatory shear testing, used to characterize the viscoelastic response of soft materials, is often divided into small, medium, and large amplitude oscillatory shear (SAOS, MAOS, and LAOS) regions. SAOS is a common test that gives us a unified analysis and interpretation of linear viscoelastic behavior, whereas understanding MAOS and LAOS is still an active area of research. While numerous mathematical techniques have been proposed, a consensus interpretation is still missing. Recently, our understanding of nonlinear behavior in the LAOS regime has been developed using iterative recovery tests. Recovery rheology decomposes the strain into two components, allowing an unambiguous interpretation of the nonlinear behavior in terms of sequences of recoverable and unrecoverable processes. In this work, we revisit the MAOS material functions for polyvinyl alcohol-borax hydrogel and worm-like micelles using recovery rheology. We show that two mathematical formalisms, the Chebyshev and sequence of physical processes analyses, provide competing physical interpretations when they are derived from the total strain, but provide unified interpretations when describing the decomposed strains. We, therefore, show that what has often been treated as a mathematical problem can instead be solved experimentally by acknowledging the extra information provided by recovery rheology.