Kramers-Kronig Relations for Nonlinear Rheology: 2. Validation of Medium Amplitude Oscillatory Shear (MAOS) Measurements

TL;DR

This paper introduces a validation method for nonlinear rheology data using Kramers-Kronig relations, enabling better analysis of material behavior through MAOS measurements even with noisy or limited data.

Contribution

It develops the SMEL test, a novel statistical fitting technique for validating MAOS data and identifying time-scale regimes in nonlinear rheological measurements.

Findings

SMEL test effectively validates MAOS data across various materials.

The method can handle noisy or limited frequency data.

It helps identify timescales where TSS holds in materials.

Abstract

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 fitting technique called the SMEL test, which 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 timescales over which a material exhibits TSS.