MITlaos: Understanding Large Amplitude Oscillatory Shear (LAOS)

We have developed a framework for physically interpretating Large Amplitude Oscillatory Shear (LAOS), to make a rheological fingerprint of a complex material.

For many systems the common practice of reporting only "viscoelastic moduli" as calculated by commercial rheometers (typically the first harmonic Fourier coefficients G1' , G1") is insufficient and/or misleading in describing the nonlinear phenomena. Although the higher Fourier harmonics of the material response capture the mathematical structure, they lack a clear physical interpretation.

Part of the framework gives a physical interpretation to the third-order Fourier coefficients. We build on the earlier geometrical interpretation of Cho et al. (2005) which decomposes a nonlinear stress response into elastic and viscous stress contributions using symmetry arguments. We then use Chebyshev polynomials (closely related to the Fourier decomposition) as orthonormal basis functions to further decompose these stresses into harmonic components having physical interpretations.

We also introduce new measures for reporting the first-order (linear) viscoelastic moduli. These measures give deeper physical insight than reporting only the first harmonic Fourier coefficients G1', G1", and reduce to the linear viscoelastic framework of G', G" at small strains.