MITlaos: understanding Large Amplitude Oscillatory Shear (LAOS)
R. H. Ewoldt, A. E. Hosoi, G. H. McKinley
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 our 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
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.
Software is available for analyzing raw data with this framework. To request the free software, please contact MITlaos [at] mit [dot] edu.
Also see Randy Ewoldt's personnal webpage.