Large amplitude oscillatory shear (LAOS) test has been used to elucidate the nonlinear viscoelastic behaviors of soft matter or complex fluids under large and rapid deformations encountered in production and application, especially for most polymeric materials. In this work, combined with recovery rheology, the physical visualization of the start and end yield stress values of yield stress fluids determined by the algebraic stress bifurcation (ASB) method is further interpreted in extenso. Facing the issue of unrecoverable deformations that may occur below the yield stress, the ASB method suggests the start and end yield stresses by considering the timescale, thereby linking the yield stress determination and nonlinear behavior analysis in LAOS. The unusual sharp corners in the Lissajous curves induced by the Kamani–Donley–Rogers (KDR) model are also revealed and treated by viscosity regularization. The correlation among the yield points determined by ASB and stress bifurcation, the responses of the KDR model, and corresponding results and insights by main LAOS analyses in representative cases are comprehensively discussed. This work contributes to a new understanding of stress bifurcation.
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