  In this work we study onset of nonlinear rheological behavior of a colloidal
dispersion of a synthetic hectorite clay, Laponite, at the critical gel state
while undergoing sol-gel transition. When subjected to step strain in the
nonlinear regime, the relaxation modulus shifts vertically to the lower values
such that the deviation from linearity can be accommodated using a strain
dependent damping function. We also perform creep-recovery and start-up shear
experiments on the studied colloidal dispersion at the critical gel state and
monitor deviation in response as the flow becomes nonlinear. A quasi-linear
integral model is developed with the time-strain separable relaxation modulus
to account for the effect of nonlinear deformation. Remarkably, the proposed
model predicts the deviation from linearity in the creep-recovery and start-up
shear experiments very well leading to a simple formulation to analyze the
onset of nonlinear rheological behavior in the critical gels. We also analyze
the energy dissipation during the nonlinear deformation and validate the Bailey
criterion using the developed viscoelastic framework.
