Polymer brush under strong shear

End-grafted polymer brush exposed to strong shear solvent flow is studied. Under strong enough shear flow, the shear force is nonlinear with the blob size depending on the shear force and not on the monomer volume fraction $\phi$. We derive the crossover force scale separating the weak and strong shear regime. The velocity profile of the flow, $v\left(z\right)\mathrm{}$, inside and above the brush is calculated analytically by treating the flow as in a porous medium and solving the Brinkman equation. The solution of the velocity profile is then combined with nonequilibrium Monte Carlo simulation data, which allow a self-consistent determination of the chain end-to-end length and the incline angle of the chain. We derive the scaling form for the chain positions $x\left(n\right)\mathrm{}$ for the $n\mathrm{th}$ monomer and verified by our simulation data. We further obtain analytical expression for $x\left(n\right)\mathrm{}$ in terms of the effective viscosity of the model.