[Physics] If fluids have zero shear modulus, how to make sense of graphs like strain rate vs shear stress (to classify fluids as Newtonian or non-Newtonian)

Question

Following the definition on the wiki: Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it.

If fluids have zero shear modulus, shouldn't the shear stress be zero regardless of the strain rate?

Thanks

Answer 1

Solids have a shear modulus that relates the shear stress to the shear strain. Liquids have a viscosity that relates the shear stress to the shear strain rate. Apply a shear stress to a solid and it deforms a bit, reaching a new equilibrium shape that remains motionless until the stress is removed. Apply a shear stress to a liquid and it continues to deform at a constant rate until the stress is removed. No matter how small the stress, the strain will become arbitrarily large given enough time: shear modulus of liquids is zero.