  We investigate the nonlinear viscoelastic behavior of a colloidal dispersion
at the critical gel state using large amplitude oscillatory shear (LAOS)
rheology. The colloidal gel at the critical point is subjected to oscillatory
shear flow with increasing strain amplitude at different frequencies. We
observe that the first harmonic of the elastic and viscous moduli exhibits a
monotonic decrease as the material undergoes a linear to nonlinear transition.
We analyze the stress waveform across this transition and obtain the nonlinear
moduli and viscosity as a function of frequency and strain amplitude. The
analysis of the nonlinear moduli and viscosities suggests intracycle strain
stiffening and intracycle shear thinning in the colloidal dispersion. Based on
the insights obtained from the nonlinear analysis, we propose a potential
scenario of the microstructural changes occurring in the nonlinear region. We
also develop an integral model using the time-strain separable K-BKZ
constitutive equation with a power-law relaxation modulus and damping function
obtained from experiments. At low strain amplitudes, this model compares well
with experimental data at all frequencies. However, a stronger damping
function, which can be efficiently inferred using a spectral method, is
required to obtain quantitative fits across the entire range of strain
amplitudes and the explored frequencies.
