Strain-Rate Frequency Superposition in Large-Amplitude Oscillatory Shear

TL;DR

This paper investigates strain-rate frequency superposition in soft solids under large-amplitude oscillatory shear, demonstrating that nonlinear viscoelastic properties can be superimposed onto master curves similar to linear regimes.

Contribution

It extends the strain-rate frequency superposition concept to large-amplitude oscillatory shear in soft solids, showing superposition of higher harmonic moduli with the same shift factors as linear viscoelasticity.

Findings

Higher harmonic moduli can be superimposed onto master curves.

Energy dissipation depends solely on the first harmonic loss modulus.

Behavior at low frequencies in LAOS resembles that at high strain amplitudes.

Abstract

In a recent work, Wyss, {\it et.al.} [Phys. Rev. Lett., {\bf 98}, 238303 (2007)] have noted a property of `soft solids' under oscillatory shear, the so-called strain-rate frequency superposition (SRFS). We extend this study to the case of soft solids under large-amplitude oscillatory shear (LAOS). We show results from LAOS studies in a monodisperse hydrogel suspension, an aqueous gel, and a biopolymer suspension, and show that constant strain-rate frequency sweep measurements with soft solids can be superimposed onto master curves for higher harmonic moduli, with the {\it same} shift factors as for the linear viscoelastic moduli. We show that the behavior of higher harmonic moduli at low frequencies in constant strain-rate frequency sweep measurements is similar to that at large strain amplitudes in strain-amplitude sweep tests. We show surface plots of the harmonic moduli and the energy dissipation rate per unit volume in LAOS for soft solids, and show experimentally that the energy dissipated per unit volume depends on the first harmonic loss modulus alone, in both the linear and the nonlinear viscoelastic regime.