Isolating the Medium Amplitude Oscillatory Shear Regime via Constitutive Modeling

Medium amplitude oscillatory shear (MAOS) represents an elegant compromise between small amplitude oscillatory shear, which probes only linear viscoelasticity, and large amplitude oscillatory shear (LAOS), which can be compromised by experimental artifacts and challenges in interpretation. However, extracting MAOS moduli from experimental data remains challenging due to the narrowness of the accessible strain amplitude window and the need for laborious extrapolation to filter out noise and contamination by higher harmonics. We present a computational framework that bypasses this bias-variance trade-off and shifts experimental burden to numerical analysis, enabling robust extraction of MAOS moduli from conventional LAOS measurements. Our approach combines two key elements: (i) discovery of constitutive models from LAOS data using sparse polynomial approximation, and (ii) Richardson extrapolation with successive refinement to isolate the asymptotic MAOS response. We demonstrate this methodology using worm-like micelles as a model system. The discovered constitutive models accurately reproduce relevant experimental data and enable systematic exploration of the frequency-dependent MAOS moduli. This framework is general and can be applied to any soft material, offering a pathway to make MAOS characterization more accessible by automating the most labor-intensive aspects of traditional experimental workflows.