Fluids for which the viscosity increases with the rate of deformation (du/dy) are called shear thickening or dilatant fluids.
These are the non-Newtonian fluids i.e. the relationship between shear stress and shear strain rate is non-linear.
These two videos show examples and demonstrations of the non-newtonian fluids
1. Newtonian vs. Dilatant fluid
2. Non-Newtonian Fluids