New insights into tackling large amplitude oscillatory shear from an analytic perspective

Large amplitude oscillatory shear (LAOS) has been widely applied for performing rheological analysis of complex fluids, especially yield stress fluids (YSFs) encountered in nature, daily life, or industry. The Fourier transform (FT) rheology is considered one of the mainstays in LAOS since FT is an essential mathematic tool applied in numerous signal analysis fields. However, the challenge of understanding FT, diverse mathematical frameworks, and complicated data processing impede the intuitive accessibility and efficient implementation of the existing, even admirably successful LAOS methods. Thus, developing novel LAOS methods and simplifying methodology remain an unmet need. In this context, motivated by analytic geometry using coordinates instead of geometries, an analytical perspective in LAOS was highlighted by abstracting Fourier coefficients from stress/strain waveforms and substituting them into analytical solutions of LAOS methods, thereby proposing a new analytic LAOS (aLAOS) approach to tackle LAOS by reversely using the methodology of FT rheology. More specifically, the rheological signals and measures can be precisely reconstructed using Fourier coefficients instead of processing stress/strain waveforms. The influences of even harmonics on LAOS methods were described. Furthermore, considering the acquired results from the LAOS tests on the various typical YSFs, it was demonstrated that the aLAOS method yielded the same results as other methods and could visually distinguish the contribution of arbitrary higher harmonics. Consequently, this approach was potentially an alternative for a non-trivial candidate for the convenient treatment of LAOS, thus utilizing it as a tool to assist in the calculations of existing methodologies.