Kramers-Kronig relations for nonlinear rheology. Part II: Validation of medium amplitude oscillatory shear (MAOS) measurements

The frequency dependence of third-harmonic medium amplitude oscillatory shear (MAOS) modulus G 33 * ( omega ) provides insight into material behavior and microstructure in the asymptotically nonlinear regime. Motivated by the difficulty in the measurement of MAOS moduli, we propose a test for data validation based on nonlinear Kramers-Kronig relations. We extend the approach used to assess the consistency of linear viscoelastic data by expressing the real and imaginary parts of G 33 * ( omega ) as a linear combination of Maxwell elements: the functional form for the MAOS kernels is inspired by time-strain separability (TSS). We propose a statistical test based on fitting a sum of Maxwell elements using LASSO (least absolute shrinkage and selection operator) regression, and call it the SMEL test. It works well on a broad range of materials and models including those that do not obey TSS. It successfully copes with experimental data that are noisy or confined to a limited frequency range. When Maxwell modes obtained from the SMEL test are used to predict the first-harmonic MAOS modulus G 31 *, it is possible to identify the range of time scales over which a material exhibits TSS. (C) 2022 The Society of Rhealogy.