  Large amplitude oscillatory shear (LAOS) has been widely applied for
performing rheological analysis of complex fluids, and the Fourier transform
(FT) rheology is considered one of the mainstays in LAOS since FT is an
essential mathematic tool that is applied in numerous fields of signal
analysis. However, the challenge of understanding FT, diverse mathematical
frameworks, and complicated data processing render existing LAOS methods hard
to be effectively used. As a result, their accessibility and implementation are
limited in practice. Thus, the development of novel LAOS methods remains an
unmet need. In this context, a newly analytic LAOS (aLAOS) approach was deduced
here to tackle LAOS by the reverse use of the methodology of the FT rheology.
More specifically, the rheological signals and measures can be precisely
reconstructed based on the established equations involving Fourier coefficients
instead of processing numerous discrete points of the Lissajous curves.
Furthermore, considering the acquired results from the LAOS tests on the
various typical yield stress fluids, it was demonstrated that the aLAOS could
unify the mainstream LAOS methods into one Fourier coefficient-based framework
and visually distinguish the contribution of arbitrary higher harmonics.
Consequently, the proposed approach is arising as a promising candidate for the
convenient treatment of LAOS, which could also highly promote the multi-field
applications of LAOS.
