  Using a combination of theory, experiment and simulation we investigate the
nonlinear response of dense colloidal suspensions to large amplitude
oscillatory shear flow. The time-dependent stress response is calculated using
a recently developed schematic mode-coupling-type theory describing colloidal
suspensions under externally applied flow. For finite strain amplitudes the
theory generates a nonlinear response, characterized by significant higher
harmonic contributions. An important feature of the theory is the prediction of
an ideal glass transition at sufficiently strong coupling, which is accompanied
by the discontinuous appearance of a dynamic yield stress. For the oscillatory
shear flow under consideration we find that the yield stress plays an important
role in determining the non linearity of the time-dependent stress response.
Our theoretical findings are strongly supported by both large amplitude
oscillatory (LAOS) experiments (with FT-rheology analysis) on suspensions of
thermosensitive core-shell particles dispersed in water and Brownian dynamics
simulations performed on a two-dimensional binary hard-disc mixture. In
particular, theory predicts nontrivial values of the exponents governing the
final decay of the storage and loss moduli as a function of strain amplitude
which are in excellent agreement with both simulation and experiment. A
consistent set of parameters in the presented schematic model achieves to
jointly describe linear moduli, nonlinear flow curves and large amplitude
oscillatory spectroscopy.
